you can't restrict standard equipment that do not send a character into a higher tier, so I will be operating under the assumption that Kratos is fully equipped, also we dont know how powerful War is with the seals broken nor is there a key for that, so I will assume second key war
AP/Dura/SS: pretty much equal, War upscales from 24 Megatons while Kratos scales to 30 Megatons so this is pretty much a non-factor
LS: Class K vs Class G, Kratos steamrolls in this department
Stamina: pretty sure War has the advantage, but this fight will be done within an hour so stamina is also a non-factor
experience and skill: Kratos's feats are impressive, being a spartan commander and all of that, unfortunately War has untold millennia of combat experience, mostly facing people who could give him a good fight or just genociding entire planets, and War is also noted to be a better tactician then Death by the pale-skinned man himself, while The Abomination Vault's canon with the rest of Darksiders is questionable at times we can take quite a bit of it as truth.
overall and fight: Kratos has the hax to overwhelm War, unfortunately Kratos might be dead by the time he gets to using his Hades shit, and if Kratos manages to kill War the ladder just gets right back up with undying and continues the fight, the issue is actually killing War will take using the Hades thing due to War having that skill advantage, Kratos swings with the blades of Chaos, War finds out their range almost immediately, and proceeds to bully Kratos in melee until Kratos is dead with his skill, instinctive reaction, and speed
TLDR: War outskills, has instinctive reaction, and has the speed advantage to crush Kratos in Melee before the ladder haxes him to death
War Mid-diff