Standard powers of the Olympians, plus the God of War specific ones that Ares demonstrated. Though we haven't really seen what Kratos can do in God Form outside of Betrayal perhaps (I haven't played it, so don't hold me to that).
God Kratos is presumably a much more powerful version of Kratos.
~ In addition to his God Form, he also has access to all his weapons/magics/relics.
The Blade of Olympus, The Gauntlet of Zeus, The Blade of Artemis, & The Blade of the Gods were all capable of killing Gods (presumable, in the case of Artemis), with the BoO practically being a 'walking' Deus Ex Machina, meh.
It's also arguable that he has Pandora's Box to amp himself(???)
Originally posted by NemeBro
God of War Kratos would logically have all of Ares' powers, such as killing an army of Barbarians with a clap of his hands, combusting them, popping their skulls, lifting them into the air, etc.
Lifting them into the air...forgot that one, an example of 'subconscious' TK?