Kratos has vastly varying levles of power. At his weakest, he's not even aware of his true natural abilities and is mashing enemy soldiers' heads on a rocky wall and leading a fifty man army in conquest (, at his strongest, he's the size of a mountain and sitting on a throne with women by his feet (who were actually the same ones from the first God of War if you look closely lol), and at his base level, he's killing legendary Greek heroes with a door.
I'd say he has the resources and abilities to brave anything that Dante has in DMC3, most of the time, Kratos' brute strength alone was the only thing attesting to his victories. Heck, Kratos even had a duel with Zeus that was (for the most part) similar to Dante's duel with Vergil (the one where Dante's DT was awakened for the first time. Mission 7 IIRC, that heartwarming family reunion).
With the exception of his "ultimate reward", Kratos probably at his most powerful at the end of God of War 2. He wields not only the Blade of Olympus (which holds his powers as the God of War) and Titans' powers but he also has full control over time and destiny.