Someone made a good point. Ares, the ousted God of War, was killed by Kratos, a human. A super powered up, blessed by the gods human, but still human nonetheless. Was he stabbed in the gut or something? I can't really remember. So, gods can be killed, just as Dante can.

However, Dante has been stabbed numerous times in his life. Play Devil May Cry 3 for 5 minutes, and you see him get 'fatally' stabbed at least twice in cutscenes. The 2nd time, he proceeds to eat pizza and kick demon butt, using the broken shards of sharpness in his body to kill them. Let's see Kratos do that.

If it were a Ranged Battle, Dante would have the advantage. He can fire faster than Kratos can throw his lightning bolts, and his ammo is unlimited. Dante can keep himself distanced from Kratos to continuously pelt him with bullets from afar, which would probably end in a stalemate.
Even up close, Kratos wouldn't be a clear winner. Dante can dodge just as Kratos can, and while Kratos is stuck doing his big elaborate combo, Dante can poke him a few times from behind with a weapon of his choice.

I dont' think Kratos would know how to deal with bullets anyway, and he certainly doesn't know how to deal with Pizza.

Advantage: Dante