1. timeline - if I remember, all of battles done by Kratos were during ancient times of Greece while apocalypse waged by War was done in present time, so who knows what happens to Kratos in the meantime
2. skills - both are more than just skilled, using various weapons to achieve pure massacre of enemies and both back hell of a punch as we have seen all too well .
3. and this is the most baffling part... how would a battle conclude where "God of war" meets "war itself". Do you easily tame what you rule or can you even battle the tool.
Still as I didn't play God of war (PC fan and I did play Darksiders), though from all youtube videos of gameplay and I would say that War has slight advantage. Kratos was mortal to ascend while War already belongs to almost extinguished race that is now the main force of the Council above Heaven and Hell... so it gotta count for something.
I am not saying it will make easy battle, too many variables and it would be impossible to actually predict winner... but it would sure be one hell of a long and epic battle and I would be surprised if entire planet doesn't explode from the first clash of swords