Kratos vs Wonder Woman: A Quick Breakdown

So the other day I was actually asked about this matchup and I found it's a matchup that has some substantial interest. It's easy to see why. Kratos and Wonder Woman are both characters with heavy Greek Mythological origins, both famously killed their universe's Ares, the God of War before becoming the new God of War. And both fight with an iconic long thin mid-range extended melee weapon that can grapple things. I love both Kratos and Wonder Woman, they both are probably in my top 20 favorite characters of all time so I made this blog as a quick breakdown for those interested on my thoughts on the fight.

This will be God of War 3 Kratos with Pandora's Box Amp + God of War Powers vs the current Rebirth Wonder Woman, with goddess of war powers. These are the strongest version of the two characters that can be considered standard.

Strength/Durability:

Kratos in God of War is scaled to characters like Thor and Jormungandr including matching Baldur in strength who knocked down Jormungandr. In their fight Thor and Jormungandr will "splinter" the world tree Yggdrasil

a cosmic tree containing the Norse Pantheon's realm including 9 different dimensions as well as the realm between realms

This Kratos is considered weaker than Base Kratos from God of War during his fight with Zeus and is stated in the novelization to be "less muscular"

which makes sense given he easily is able to fight Zeus who far outscales pretty much anyone in the Greek Pantheon who themselves can threaten the entire Greek Pantheon's realm containing multiple dimensions. Zeus and Kratos are suggested by two developer statements to be able to fight Polygon Man, a Sony Playstation Crossover villain capable of fusing dozens of dimensions together

Admittingly, these are twitter word of god statements and one of them at least seems fairly unsure, so it's understandable if you don't agree with their usage. However given the other feats Kratos has including scaling to characters that can destroy a structure significantly larger than 9 dimensions, it seems fairly consistent and moreso just supporting.

Wonder Woman as of DC Rebirth is pretty regularly shown to be relative strength-wise to Superman and Supergirl knocking back Superman villain Doomsday with a shield bash and having an extended fight with a brainwashed Supergirl

As of Rebirth, as confirmed numerous times, all events have been made canon again to the mainline DC Earth. Within the Pre-Crisis continuity Supergirl when pushing herself to her absolute limit was able to damage the armor of the Anti-Monitor and made him flee

Anti-Monitor being a cosmic threat who even at this point had fought his equal and opposite enemy the Monitor for 1,000,000 years to a standstill, the Monitor being an entity powerful enough that with his dying energy he created a netherverse to hide the last remaining dimensions within from the Anti-Monitor

Comparing their base power, I think Kratos has a pretty clear advantage. Wonder Woman scales to a structure capable of containing two dimensions while Kratos scales to mascroscopic structures that contain nine dimensions and more, or to villains that can fuse dozens of dimensions. While both characters scale "above" their respective feats, I think Kratos probably has more raw strength and durability. Not neccesarily an insurmountable difference. I think Wonder Woman's strikes would probably do some damage to Kratos and I don't think Kratos would kill Wonder Woman with one strike but I think if they got into a strength competition, Kratos would win.

Both can also get stronger but I think Kratos also has a higher raw power amp. Wonder Woman can remove her bracelets to boost her power being normally evenly matched to Artemis while stomping her in a different fight when she removes her bracelets.

Kratos' rage is a similar type of power-up, used to amplify all his stats

to a significant enough degree as to allow him to stomp enemies that were previously evenly fighting him or had the advantage such as fighting Thanatos' humanoid form with difficulty with Deimos to stomping his monster form by himself

This would be by itself equal to Wonder Woman's own amp, but Kratos also has the stronger Power of Hope amp which eclipses it going from being easily killed by two-fingers of Fear Zeus despite his rage amp to Fear Zeus being unable to damage him.

Both also have implications of scaling to infinite quantities. 

I personally don't really use that as it is not logically consistent for a quantity to be finitely above or below an infinite quantity, and both Kratos and Diana have characters that are finitely weaker and stronger than them. At worst I think it equalizes out for both of them.

Speed:

In terms of movement speed, Kratos scales to the Fates who have the incredible movement speed feat of controlling the fates of all things in the entire Greek realm down to every animal motion and landscape movement

This is a speed feat calced anywhere in the range of quadrillions to septillions of times the speed of light.

Even more immense than this, Kratos in short burst speed, as well as reaction/attack speed can reach the speed of Hermes even as early as God of War 1

Hermes delivers all dreams to all mortals and all souls to the Underworld. He is, humorously for this comparison, the "Flash of Greek Mythology"

This comparison would be made more apparent when Kratos actually reacted to and killed Hermes directly. Hermes scales to Atropos' astral projection which moved to Olympus at "infinite speeds"

Wonder Woman is one of DC's greatest speedsters. Even in the Post-Crisis era she famously blocked the trillions of shards sent by the shattered god across the universe instantly, a feat calced at quintillions of times the speed of light and is considered relative to a Superman that stopped missiles threatening to blitz the universes at speeds calced at sextillions of times the speed of light

And as of Rebirth is capable of matching speed force users and Pre-Crisis Kryptonians that could travel infinite lengths in finite time as well as moving fast to enter into the speed force, the conceptual realm of the multiverse's speed via the speed of the God Mercury granted to her

If you don't think the infinite speed applies here that's fine though I think it's different because God of War's infinite speed doesn't seem to have any characters be finitely higher or lower than it and DC's infinite speed is conceptual in nature. 

So comparing them speedwise, Wonder Woman seems to have speed roughly on par with Kratos' burst speed, his reaction/attack speed. To put this in the terms of both universes, Wonder Woman would be like fighting Hermes for Kratos speed-wise as she would have a similar level of speed which is more than Kratos, which allowed Hermes to evade him casually at distance, but which Kratos could tag him in close range.

Conversely for Wonder Woman this would be like fighting Starfire who has the reactions times from her superhuman skill level to tag speedforce users, and can fight Wonder Woman in fisticuffs, but doesn't have that level of movement speed herself. 

Skill:

Kratos and Wonder Womans' best skill feats happen to sorta be the same thing, though in context its different because of the different universes they inhabit. Kratos and Wonder Woman both killed Ares, the God of War and scale to Ares in skill.

In God of War 1, after Ares completely depowers Kratos leaving him with nothing but his stats gained from Pandora's Box, (10:35) Kratos is still able to kill Ares via his skill (11:25)

Ares was a millenia old warrior who had, and which Kratos gained after becoming the God of War, a cosmic awareness of all combat through history for at least thousands of years. (5:00) The God of War Universe is a massive world where combat seems to be very common comparatively, meaning this would likely be equivalent to millions of years of combat experience, roughly a Mid A Tier level of skill by the quantification method I use for skill.

However Wonder Woman's feat is even more extreme. She was also able to kill the God Ares, and had to fight him multiple times despite his significant power advantage

While God of War Ares is a physical immortal entity presiding over warfare, DC Comics Ares is literally the concept of warfare  with knowledge of every single strategy and tactic from every battle since the beginning of time, across billions of years and an infinite multiverse. It's no surprise that Diana is the best melee fighter on the DC Earth.

Skill-wise, Wonder Woman had the advantage.

Intelligence:

While both characters have radically superhuman skill, their general intelligences are a lot more realistic, if still impressive compared to a normal human's

Kratos' intelligence is often downplayed in vs debates. While Kratos in the Greek Era does have a tendency of allowing his rage to get the better of him, he is of fairly high general intelligence. Kratos led the armies of Sparta to widespread militaries victories across Greece, and after becoming God of War would continue to guide them to war. He is inventive with using his environment in ways to get strategic advantages, and has solved numerous difficult puzzles in his travels including the puzzles of Daedalus meant to guard the most important objects in the verse as well as the Goddess Hera's spatial puzzle that she claimed would trap him forever. And given he was at the time an immortal God, she could indeed mean she intended for it to trap him FOREVER.

Wonder Woman is regularly considered one of the wisest members of the Justice League, granted wisdom as a gift by the Goddess Athena upon her birth, and is regularly consulted by even characters like Batman for council. She has had to regularly foil schemes by immortal supervillains like Circe and Ares and her wisdom has given her a knack for strategy, leadership, and diplomacy. She was able to beat the insane genius the Joker by out-crazying him, and once defeated Ares simply by showing him the results of his own warfaring ways would leave a war barren of people with no longer any ability to war.

Comparing them in intelligence, I don't think there's any huge gap. I think that while both are probably similarly skilled in strategy and tactics I think Wonder Woman is perhaps more versatile in her intelligence and probably has a greater scientific knowledge and a greater wisdom than Kratos. Though the two are relative enough that I don't think it would make that large a difference. 

Range:

Kratos typically uses weapons with extended melee range like the Blades of Chaos or close range projectiles on the scale of tens of meters. In his giant form, Kratos would have an effective range of many kilometers purely from size. However his maximum range is vastly higher. As the God of War he should scale to Ares who not only threw a rock spike from Athens ahitting Kratos with extreme precision all the way in the Desert of Lost Souls far to the East of Athens but was also able to affect Kratos while Kratos was in another dimension 

Wonder Woman typically uses weapons in extended melee range like the Lasso of Truth or closer range projectiles on the scale of tens of meters. By banging her bracelets together she can create a thunderclap that can extend for kilometers and similarly her lightning manipulation can effect structures as massive as mountains. Her Lasso of Truth can affect the entire universe at once and with her god powers she can technically manipulate Mount Olympus even from another dimension, though these does not seem to be combat-useable powers. 

So in terms of range both Kratos and Wonder Woman tend to fight at a very similar range via extended melee range weapons (Chained Blades and Lasso.) However beyond that point Kratos definitely has that advantage. In his giant form Kratos can use all his abilities at a range of kilometers whereas Wonder Woman can only use a few abilities at such a range (though in fairness against a giant target like Giant Kratos, accuracy at range will be less of a concern.) While both can technically summon things from an inter-dimensional range, and affect things on an inter-dimensional range, only Kratos seems to be able to attack from that far a range. While Post-Crisis Ares demonstrated that ability, it was an ability Wonder Woman struggled with and which New 52 Ares, the one she got the powers of, did not demonstrate.

Endurance/Stamina:

Kratos regularly takes brutal beatdowns and is severely damaged and continues to fight and recovers quickly. He was able to persist even without his god powers after being smashed by the hand of the Colossus of Rhodes, survived being impaled by the Blade of Olympus, and recovered quickly from a bloodying fight with Baldur, aided by his regeneration. He was also able to climb for three days straight even as a Demigod. 

Wonder Woman has been beat down immensely, especially by Bizarro and Ares both with the intent to kill her and as being hit by the full force of Superman's Heat Vision from the Sun to Earth when Superman was mind controlling into thinking Wonder Woman was Doomsday. She also fought demons with Superman and Thor in Asgard for 1,000 years. 

In terms of physical endurance I think Kratos has the advantage. Wonder Woman's endurance seems relatively speaking moreso peak human or low superhuman FOR her durability. As in she survives physical wounds generally speaking similar to what a tough human could survive or attacks from people somewhat stronger than her. Conversely Kratos has been completely impaled before without dying, and has endured strikes from people massively stronger than him.

In terms of general stamina, I think Wonder Woman has a much higher feat of fighting for 1,000 years vs climbing for three days, though I don't think this is a fight that would go on for days and neither can really tire the other one out as a win con so while Wonder Woman has the advantage it's not a super useful one.

Now just going to go over their capabilities in three categories and suggest how I think each ability would or would not work on the other, separated into Divine Abilities, Magic, and Equipment. These are mostly just focusing on what I think are their strongest abilities as both have plenty of random abilities.

Divine Abilities:

Kratos is known for his legendary rage which bolsters his abilities and can envelop him in an aura

The various auras around Kratos wouldn't be too difficult to deal with for Diana who typically fights with weapons regardless but Kratos' ability to rapidly improve as the God of War would present a challenge overtime as if the fight goes on too long, Kratos will eventually just overwhelm Diana as she doesn't have a similar power to improve her capabilities rapidly unless she uses the godwave.

Kratos is an immortal deity with a natural healing factor able to recover from wounds like massive holes in his chest. 

As mentioned above Wonder Woman has divine weapons capable of killing Gods of similar immortality and greater regenerative properties

Kratos regularly absorbs the life, energy, and magic from his enemies in the forms of orbs which he can do even with his bare hands

Wonder Woman has a limited resistance to this type ability. The Supervillain Clayface was able to absorb Wonder Woman's life and abilities and Wonder Woman was able to break out of it even after being reverted to clay

However this did take some time, so presumably Kratos would be able to somewhat absorb lifeforce and magic from Wonder Woman.

Kratos likely has all the powers of the prior God of War Ares. Ares showed the ability to create pseudo-black holes that could suck people into his dimension he could reality-warp within, create dark duplicates and steal Kratos' abilities

Wonder Woman has on numerous instances resisted the pulls of Black Holes, and was able to fight the God Ares in his own dimension the Areopagus where he can control reality and not even Zeus can touch him showing a level of reality-warping resistance

However it was highly difficult on Wonder Woman. Beyond that she has never shown resistance to power-stealing as comprehensive as God of War Ares'. It's unclear if Kratos would be able to create dark duplicates of Wonder Woman as she is not psychologically conflicted the way Kratos was at the time of the battle, and she has fought an evil duplicate of herself several times, but if he can that it would obviously be a large advantage just for dividing her attention. If Kratos manages to pull Wonder Woman into the other dimension, he would be at a massive advantage tactically.

Kratos' strongest divine power is the Power of Hope which laid dormant within him

The Power of Hope is the conceptual hope that is the greatest power of the Greek Realm at least. It grants Kratos a massive power amp, the ability to affect conceptual entities among other things. It also grants makes Kratos functionally unkillable as it can allow him to bring himself back to life from his own determination. This means for Wonder Woman to defeat Kratos she would need to either break his resolve which, while Wonder Woman is an immensely good advocate for peace who even quelled Ares' spirit, is just not happening to Embodiment of Rage God of War 3 Kratos outside very specific circumstances. Or she would need to destroy the power of hope itself, or destroy Kratos in body and soul. Both of which are hypothetically possible for Wonder Woman but very difficult and not what she would want to do.

Wonder Woman was granted many divine gifts by the Gods including Demeter giving Diana her strength, Athena granting Diana her wisdom, Hermes granting Diana her speed and flight, and Aphrodite granting Diana her beauty and loving heart. However Artemis and Hestia both also granted her gifts. As part of her gift from Artemis she was given oneness with animals able to communicate with them and ask them to heed her call. Depending on where they fight this could be an actual weapon as both universes do have some "animals" that are relevant physical threats to them

However Kratos has acquired the Head of Danaus which allows him to command animals as well, canceling out the potential advantage.

Hestia granted Diana the most esoteric of the gifts, sisterhood with fire such that she may open men's hearts. Wonder Woman can alight her lasso of truth with a purifying flame that can kill even the undead Black Lanterns and can keep the impure from crossing its threshold

God of War 3 was the low point of Kratos' life as a person where he brought destruction unto the world for his insatiable need for vengeance. While he does have resistance to conventional flame, Wonder Woman's purifying flames I think might be able to actually kill Kratos due to his own evil.

In her Goddess State, Wonder Woman can surround herself with a battle aura similar to Kratos' rage aura

though I think Kratos should be durable enough to withstand it, even ignoring that he usually fights with weapons at extended melee range.

As the Goddess of War, Diana can communicate telepathically with every soldier, and should have the same ability as New 52 Ares, who was able to summon every soldier who ever lived as ghosts to fight for him

Given that this is the DC Universe this would likely include many ultra-powerful beings though none are seen. Kratos shouldn't have any particular trouble dealing with souls as he's killed souls with his bare hands before along with other intangible entities

Similar to Kratos, Wonder Woman can manipulate her own Olympus dimension that existed during the New 52 restoring it after it destruction

Similarly Kratos persisted in Ares dimension though Ares seemed to not be trying to kill him directly at that point, and instead trying to break his spirit and did succeed at taking Kratos powers away. If Wonder Woman can bring Kratos to Olympus, then she will similarly to his dimension have a massive tactical advantage.

Gods like Wonder Woman can also channel the power of the Godwave

the Godwave is the original wave of power that created all Gods in the DC Multiverse, and gives Wonder Woman the power of all the Greek Gods as she channels it

however the Godwave's full power is not meant to be held within one entity, and trying to do so for too long drives whoever holds it mad and erases them from existence meaning Diana can only briefly use this power

If Diana uses the Godwave against Kratos, she probably can kill him even with the Power of Hope as even just the power of the Greek Pantheon includes the power of Gods like Zeus that can control infinitely-sized conceptual realm in the Godsphere and equals other infinitely powerful gods and which can permanently kill conceptual entities. 

However Diana can't use it for long and has only ever channeled it through her body meaning she needs to be in melee range to use it, meaning via his reaction time and mid-range weapons if Kratos can outlast it, Kratos can keep Diana from using the godwave power on him.

Magic:

Kratos has gained numerous types of magical abilities, mostly various forms of elemental manipulation. However more notably he has demonstrated various forms of lifeforce and power drain with summons like the arms of Hades

which can also transmute living people into Underworld soldiers

I actually think Wonder Woman would be able to resist the lifeforce stealing, as she can withstand being in Hades which in DC Comics dampens the fire in ones soul, drains the light from their eyes

and has resisted transmutation before, resisted being turned into a Gorilla

Kratos can also summon various types of ghosts including Sirens which can induce madness with their song

and the Gorgon Soul which can petrify people, turning them to stone

as mentioned before Wonder Woman has resisted transmutation. She's also resisted various forms of mind manipulation on numerous instances and also has a general resistance to magic

Overall I think Wonder Woman would be able to resist Kratos' magic pretty well

Wonder Woman has learned a few magical abilities herself. She's developed the ability to travel via meditation even to the Sphere of the Gods and creates magical portals between dimensions

This doesn't seem to be able to be used for BFR purposes normally. While this could hypothetically allow Diana to escape from Kratos' dimension, she couldn't use this to bring him into her dimension.

She was able to create an illusion to disguise the Justice League as civilians

However Kratos has the Eyes of Truth, an artifact that can dispel far stronger illusions

Wonder Woman fight on the astral plane, even hitting spiritual entities like demons

However Kratos was able to resist the God Hades trying to rip out his soul and should be able to resist Wonder Woman's astral plane strikes

Wonder Woman used to have a larger degree of match, a fraction of Hecate's left within her as a witchmark, but was stolen by Circe. As it stands her magic shouldn't be anything particularly difficult for Kratos. At best it may allow her to escape from Kratos' dimension.

Equipment:

Kratos has gathered a wide range of equipment which he call forth at any time from Hammerspace. Most commonly he uses his flaming Chained Blades. Beyond that he has numerous slower, shorter-range more powerful blow type weapons like the Nemean Cestus

While it would be significantly harder to tag Diana with the Cestus compared to the blades, considering his strength advantage and their ability to create shockwaves, it may be able to one-shot her.

Kratos also has the Claws of Hades, the weapon of Hades which can steal souls, which he used to steal the soul of Hades

Very fittingly, Wonder Woman has resisted this exact type of attack from Hades whose staff can steal souls yet Wonder Woman resisted

Kratos took the severed head of the God Helios which he can use to create a blinding light flash

However Wonder Woman briefly was blind in the comics and trained to fight just as well blind as she does with her sight, even fighting the League while blind

One of Kratos strongest pieces of equipment is the Amulet of Uroborus which allows him to control time and aging in an area, aging them up until they decay, rewinding them until they're restored, or slowing down time

As an immortal unaging entity, Wonder Woman may be immune to the aging decaying property of the Amulet of Uroborus, however de-aging Wonder Woman or slowing her down in time with it should work as she doesn't seem to have resistance to these forms of attacks.

Kratos also has the Oath Stone of Orkos which allows him to create a shadowy duplicate of himself that can fight alongside him or take his place for a trap like Substitution Jutsu.

This would probably be pretty helpful in a fight against Wonder Woman just to increase the overall number of attacks Kratos can give off at any one time.

Kratos also gained the Scourge of Erinys, an artifact which can create homing voids which drain the lifeforce from enemies.

While this hypothetically could work on Wonder Woman, not only does she have the aforementioned partial resistance to this type of ability, she also can reflect it with the Bracelets of Submission

Speaking of the Bracelets however, Kratos has acquired the Golden Fleece, one of his most powerful artifacts 

With the Golden Fleece Kratos can block, absorb, or reflect any form of ranged attack, even the gaze attack of Gorgons. This would functionally cut off Diana from using any kind of ranged attack against Kratos. 

However even this pales with Kratos' strongest weapon, the Blade of Olympus

The Blade of Olympus is the divine blade capable of absorbing godly essence, rendering the immortal and mortal and with one swing can create massive energy waves capable of BFR-ing enemies to Tartarus.

I don't think the ranged component of the Blade of Olympus is as much of a threat to Wonder Woman. Not only she likely block the energy component with the Bracelets of Submission, she can teleport back from Tartarus via meditation as demonstrated above. However the bigger threat the Blade of Olympus presents is the ability to render a god mortal from a strike. The Blade of Olympus would one-shot if it gets a melee strike in.

Wonder Woman has various divine equipment she keeps on her person. 

Most famously of which is her Lasso of Truth which has a variety of usages, but most notably is its ability to compel the user and show them their whole lifespan, forcing them to confront their whole reality which can make the particularly sinful suicidal

I think Kratos might be able to resist the Lasso's mental compulsion. He has been able to resist mental manipulation such as Persephone's before

However forcing him to confront the reality of his life may work. Depending on your understanding of Kratos' character and whether you think being shown his entire life flash before his eyes including all the events that haunt him would send him into a spiral despair, which would break him out of the Power of Hope, or whether he would just be like "yeah I see that everytime I close my eyes, it doesn't do anything." My reading of how the Lasso works and Kratos' character suggests moreso the former but I'd understand a difference of opinion here.

The Lasso of Truth carries the purifying fire of Hestia that burns away even Black Lanterns, Souls, and Gods

This I definitely think would work on Kratos and if Diana binds him and uses the fires of Hestia to "purify" him on a conceptual level, I think it would present an immediate threat, with only two real counters. The Power of Hope might allow Kratos to live through this given it allowed him to regenerate from an attack of Zeus fused with the very concept of Fear.

The other way of hypothetically getting out of the Lasso's purifying fire, Kratos could use the Oath Stone of Orkos to replace the him bound with a shadow duplicate like he did to Alecto's bindings

Wonder Woman can use the Lasso of Truth to teleport others along with herself

which is pretty relevant ability given Kratos does seem to have the ability to naturally travel between dimensions needing to use outside assistance to do so normally so dimensional BFR or teleporting Kratos to Olympus where Diana would have the upper hand with her reality-warping would be viable strategies. Another reason Kratos needs to avoid letting the Lasso encircle him.

Wonder Woman wields the Bracelets of Submission which allow her to reflect any ranged attack including Nekron's Dark Lightning and the bolts of Zeus

This would allow her to avoid most forms of ranged attacks Kratos could do.

She can use them to generate shockwaves and lightning strong enough to stun the Goddess Pele

However Kratos can obviously just block this with the Golden Fleece that can block Zeus' lightning.

Wonder Woman typically carries divine piercing weapons on her person including her tiara which she can throw with enough sharpness to kill the God Deimos

as well as various divine blades. Her one post-flashpoint was made by Hephasteus cutting on the atomic scale and being sharp enough to pierce even Darkseid's Emanation

which means it's actually probably sharp enough to pierce Kratos as Darkseid's emanation is actually multiversal scaling above powerhouses like Mordru and Time Trapper.

However while her sword is probably strong enough to pierce Kratos, that doesn't mean it would kill him. As mentioned above Kratos has a powerful healing factor alongside superhuman endurance. Even in his base state, Wonder Woman would need to do more damage than Kratos has ever survived, something like slicing him in half or piercing his brain to kill him, and with the Power of Hope where Kratos can literally bring himself back to life, Wonder Woman wouldn't be able to permanently kill him via her blade. 

Weaknesses:

Kratos as of God of War 3 had one real weakness, though it is a significant one. Kratos is filled with an unstoppable rage and need for revenge that possesses him and persuades him to impulsive violent actions, blinding him to the consequences of his actions. This has caused most of his own problems.

Technically Kratos also normally has a finite level of magic from which to draw on, though through enough rage he can ignore this limitation. 

Wonder Woman, like most DC Superheroes is led by a strict moral code. While she does not carry Superman or Batman's strict compulsions against killing, she will show mercy whenever possible even when it is dangerous to do so and will strive to protect civilians from collateral damager more than protect herself. She also lacks long-range weaponry due to the Amazon code of honorness.

For a long time Wonder Woman was especially vulnerable to "piercing" weapons, however this began to be faded out near the end of the Post-Crisis period and is no longer a concern for Rebirth Wonder Woman

Conclusions:

Because this is just meant to be an overview blog I'm not gonna come to any kind of conclusive decision on who'd win, but moreso I'm going to give what I think are the best arguments for both sides because I do think you can make a fairly good argument for both sides winning this matchup

The argument for Kratos: Kratos compares to Wonder Woman in general power and speed similar to how Ares would, a greater degree of power with lower speed but enough reaction speed/skill to avoid a blitz. Wonder Woman HAS defeated Ares before, but almost always through indirect means, and always with very high difficulty. Ares is usually favored in comparison to Wonder Woman and Kratos has similar abilities in several regards. While both can't really use projectile or beam attacks due to the Golden Fleece and the Bracelets of Submission, Kratos still has long range attacks he can use such as telekinesis or power-stealing (though the latter may recall them being in his dimension) meaning at long range he can essentially attack without being counter-attacked, aided by his greater enhanced senses. At close range, any strike from Kratos will do serious damage to Diana, and if he gets a hit in with something like the Nemean Cestus or especially the Blade of Olympus he can one-shot. Kratos due to durability, endurance, resistances, and healing factor would neg most of Diana's ways of killing him. Even in base state, the only ways Diana have of killing Kratos would be her Divine Sword, channeling the Godwave (which she's not liable to do and can't do very long), or getting the lasso around him. With the power of hope only the latter two of those are viable. Contrary as the fight goes on, Kratos will become increasingly strong while Wonder Woman will be slowly worn out by getting drained of lifeforce/magic and just generally a less strong healing factor. Kratos can also create a Shadow Clone of himself to help fight or get out of a dangerous scenario where Diana has gotten the lasso around him with the Oath Stone of Orkos and can possibly create shadow clones of Wonder Woman to overwhelm her or surprise her by suddenly slowing time around her or reversing her in time to get a big hit in close range.

The argument for Wonder Woman: In God of War terms, Wonder Woman has the strength of a bare-handed Hercules who did give Kratos some trouble and a speed similar to Hermes which Kratos did have significant difficulty catching up too, plus her own powerful arsenal of abilities. Wonder Woman should be able to use her increased movement speed, speed, and better flight to dart out of range repeatedly of most of Kratos attacks. While Kratos is characteristically impulsive and led by his anger, Wonder Woman is a composed warrior who can likely manipulate him by doing something like seemingly "escaping" through a portal to draw him to Olympus where she has control. This is possible because she can probably escape from his dimension, where the same is probably not true in reverse. Her lasso if she can get it encircling him would probably be able to defeat him and if he does get in close, Wonder Woman can still potentially break out of it by temporarily channeling the Godwave and overwhelming him with multiversal strikes beyond his ability to protect from. Speaking of, without prior knowledge Kratos wouldn't know Diana could suddenly use the Godwave and make entering close range for one of Kratos' trademark brutal executions suddenly massively more dangerous for Kratos. Without prior knowledge Wonder Woman is liable to find out and be able to use Kratos' weakness quicker than Kratos would be able to find out Wonder Woman's. 

So I hope this proves helpful for anyone who was wondering, these are my thoughts on the matchup as someone whose a big fan of both characters.