Well, what's the point of the fight to begin with? Presumably each is fighting in defense of their own universe as they are champions if not heroes. If getting rid of Hulk is the key to defeating the Avengers, his being gone for even a few hours would be enough for the League to knock down the Avengers and then leave, not caring whether the Hulk came back. If the Hulk showed up in the League universe to stir trouble, the entire League and even the Legion of Doom would work together possibly even with Darkseid to find a way to get rid of Hulk. Would Hulk's strength be enough to bust him out of the Phantom Zone?

Let's posit instead that one side or another is fighting for more ambitious purposes or that they're being controlled/manipulated into fighting. That side, by default, would lose eventually if not immediately.

Let's go back to a melee of Bats vs Cap. Cap may be a natural strategist, but he's still just a soldier. Bats understanding of psychology and human behavior due to apophenia inspired by multiple encounters with criminal minds including the chaotic Joker, the Scarecrow, and the Riddler means that he would play more of a mind game with Cap by luring him away from the rest of the group to someplace dark where he can hide while having a "nice conversation" with the Cap. He would tell him all about why he became the Batman and why he has more drive to win and in turn, Cap would regale him with his own traumas in the war. This is his downfall as Batman would then turn Cap's every word around to seem as though he's a horrible person and when he's at his lowest, Batman will drop him without much of a fight, the Cap having lost much of his will.

Now as the two are composed of heroes, there is no one single victory. After one side wins, there will always be a second fight wherein they'll lose. Then the third act will involve them discovering why they're at odds and working together blah blah blah.