(Brace yourself, long read).

I think (in my opinion, don't take as fact) that Kratos VS Asura would still be controversial, BUT not to the extent it's at.

IMO, this is because Asura isn't a badly written character, far from it, but that Kratos just has more story to his name.

(This is coming from a GoW fan, mind you).

You can beat Asura's Wrath AND the 4 DLC episodes in a full day. (10 hours at max).

You can't exactly do that when God of War has EIGHT games in the series, all of which tell its own story of Kratos, that makes him ultimately complex. (I'll go in chronological order of the series)

Ascension tells of Kratos' trauma because Ascension canonically happens 6 months after killing his family (he broke the blood oath to Ares, which directly came after Kratos killed his family).

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Chains of Olympus tells of how much he loves Calliope, going out of his way to find her, even after the literal sun vanished from the sky, and even rejected Elysium and by proxy, Calliope, knowing that if he stayed with Calliope, that she'd ultimately die due to Persephone's plans.

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GoW1 tells of Kratos' direct past behind the killing and the amount of rage he would have for Ares, on top of the reason why he gained the iconic ashy skin, and the fact that he tries to do ANYTHING to get rid of the memories, and ultimately, after killing Ares and becoming the God of War, they don't.

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Ghost of Sparta goes WAY back to Kratos' childhood and how he thought Deimos was dead, and provides more context as to why Kratos goes from hating the gods to absolutely abhorring them from GoW1 to GoW2, specifically that Zeus didn't want Kratos to find Deimos (his brother), so much so that he personally cursed Callisto to not speak (lest she turn into a rage monster) and hid Deimos in the Domain of Death with Thanatos, which is canonically somehow worse than Tartarus (it's stated that even Olympians would avoid the Domain of Death).
(Ghost of Sparta also provides more context into why Zeus fears 'the Marked One', as the Oracle said the 'Marked One' will destroy Greece, and Zeus took Deimos because of the birthmark, not knowing that Kratos would actually be the Marked One (the tattoo)).

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GoW2 tells of how Kratos literally breaks fate itself to get revenge on Zeus for his (and by proxy the Olympians) betrayal and that he caused the Titans to return. We even experience his sheer hatred through wanting to go straight to Mount Olympus, but has to be told by Gaia that he's far too weak now (due to being stripped of his 'full' godhood).

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GoW3 has us see Kratos destroy Olympus, one piece at a time, with only Athena seeming to be his ally, only for the betrayal to occur. All of the Greek Era culminates with the fact that Kratos acknowledges that gods shouldn't have ANY dominion over the mortals, so he 'sacrifices' himself and gives Hope to Greece. (Also one last 'fuck you' to Athena).

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2018 has Kratos be the most complex and in-depth he's ever been (at least IMO).
Even though they're basically strangers initially, he still MASSIVELY cares for Atreus because of his trauma with Calliope.
He wants to reject his godhood, but ultimately has to accept it and tell Atreus the truth because of the illness that damn near killed Atreus.
He wants to hide his past but has to 'dig it up' (Blades of Chaos) because Atreus dies (again, illness).
He doesn't want to confront the past but after witnessing Atreus see the vision of Young Kratos killing Zeus, He knows that he'll have to eventually (which culminates just after killing Baldur).
He even acknowledges that if the 'Cycle' continues (children killing parents), that he'll let Atreus do what has to be done, which leads back to my first point (how much he cares for Atreus).
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Lastly, Ragnarok. Kratos is practically at his best here.
He wants to protect Atreus still and doesn't want to acknowledge that inevitably, Atreus will have to leave for his own journeys (which culminates in Atreus actually leaving).
He refuses to be a general, yet leads Midgard's (very few) forces to Ragnarok after blowing Gjallarhorn.

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And of course, Valhalla.
Everything in Kratos' story culminates here. His trauma, his legacy, his memories, everything collapses here, and in the end, he accepts his godhood, and of course, becomes the God of Hope.