You know after awhile I think they'd both give up. Chances are Kratos would die in the first fight, climb out of hades, they'd fight again, Kratos would get the final blow in, but oh no here Dante comes back from the dead. They both don't die.
This process would repeat several times until they figured it was pointless. (That or until Some god stepped in and pissed Kratos off) seriously though, I wonder what events would lead to a fight like this? Broken macaroni art is my guess, but then who knows.
As a side note; Dante is the son of Sparda, not Sparta. Might of been a typo but it's stuck through 4 DMCs.
... There may be a slight spoiler in the next statement, so you know ...
On that note didn't the end GoW 2 let us know Kratos is the son of Zeus? (you know the whole "a son should never want to kill his father" thing)
Veterans Day