I feel like this bears mentioning again so I should probably make a blog post about it, but anyway...
Standard battle assumptions say that unless otherwise specified they are fighting in character. In character neither of these fighters, or almost any fighter really, would instantly resort to thier ace in the hole or any particularly unusual tactics at the very begining of a fight where they don't have any sort of read on the other fighter yet.
They would almost certaintly treat each other as generic fodder until shown otherwise, and though this wouldn't take more than one or two exchanges its enough of a distinction to note that kratos isn't going to start off the fight by pulling out a medusa head or any other sort of wierdly specific move when he normally would just hack and slash his way around except when that doesn't work - and likewise for ryuku she's more likely to run in and get into a sword fight with kratos at the very start rather then try and pull a city sized scissor blade on him when for all she knows he's just some dude in face paint.
They also don't start the match with any prep time, which also includes them not having perfect knowledge on each other's abilities and weaknesses. Kratos wouldn't know to use tactics that counter regen beyond his ability to damage through until he's seen that regen in action, and ryuku wouldn't know wtf a medusa head for example does or how to avoid its effects until it comes into play, by which time it may be too late.
These aren't dbz characters or anyone else who have 'power level' sensing or combat instinct like saber that warns them to be 100% on their guard for a tough opponent, these two will need to fight for a bit just to realize that they are against serious opponents.
So again, the way I see this playing out given that they don't have knowledge of each other and are in character is that they immediately get into a melee fight, kratos will be a bit faster and land the first hit, but won't expect ryuko to tank it with regen without breaking stride and obliterate him in one shot with her own hit that lands just after kratos's does.
In a fight where kratos has full knowledge going in he surely has plenty of tricks up his sleeve that ryuuko will not have any easy eay to deal with and so he would probably win given his speed advantage, but in character with no prep time this goes to ryuko.
Edit: I actually did just go and write a blog post:
Commonly Forgotten Implications of Standard Battle Assumptions