I think these two are pretty equally matched. If it weren't for Wars crossblade i'd probably give the win to Kratos. I really think that Crossblade will be a problem. It's not very powerful but it will keep Kratos on the defensive.
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War is the physical avatar of the concept of War. Just because he dies doesn't mean violence and very other factor that creates war would stop. It would probably be significantly lessened, though, which would mean a weaker Kratos due to killing an aspect of his portfolio. o.O
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War's ultimate form basically makes him kill any demon or angel in 2 to 3 hits....he can throw a car over 30 stories high while not even being next the the building (gameplay) Samael says he could easily destroy an entire legion of the best demons hell could throw out in his original form. Uses a sword mainly, but has a scythe and crossblade style weapon and a demonic pistol for long range. Was able to rip off the wings of a rather large demon (war was about the size of its tooth) and thats all so far and i have only played the first 5 hours....
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