Like many people predicted - Batman was the winner against captain america 
 

 
Cap does put up a good fight against the caped crusader 
 
 
 

Batman laments his distain for the situation, noting the billions of lives at stake in each universe.He tries to join forces but the Captain can see no way to combat the will of the cosmic beings thats forcing them to fight. As the two toss their weapons in final battle, the pipe they stand before erupts with water as the system flushes out.

Cap's shield misses it's target, but the smaller batarang connects with Captain America's skull.
As the two are engulfed in filthy waters, Captain America is unable to protect himself, feeling the dizzying effects of a blow to the head.

Searching frantically for the colourful hero, Batman submerges beneath the water, finding the helpless warrior sinking. He scoops him, and returns to the surface