Last time I checked Banner upgraded himself to go toe to toe with the Hulk.
What does upgrading himself have to do with being his soul?
Even if Kratos was luckly enough pull out hulk's soul, Banner himself could still beat kratos himself.
Banner and the Hulk share one soul. If Kratos rips out their soul, the Hulk won't suddenly turn in Banner, they'd die. As a matter of fact Banner was only able to go against the Hulk with months of prep and that didn't even work out correctly
Going toe to toe =/= winning
Of course I already know that Hulk won, but kratos is far from being as strong hulk.
Banner's battle with the Hulk has little to do with this fight as Banner had months to prepare to fight the Hulk, he doesn't have that here and wouldn't even get chance once his soul is removed from his body