Batman and Superman usually have a healthy respect for one another, but they do occasionally fight. Superman would obviously win in terms of pure brute force, but Batman does sometimes scrape out a win with his superior intellect and tactics.
Batman's superior tactics win out once again in the final round of the Injustice: Gods Among Us battle arena. After a month of fights, it came down to the two most iconic characters in the DC Comics universe. The victor was decided by votes, but it was pretty obvious that Batman was going to win anyway.
Injustice: Gods Among Us has been available since Tuesday, and early reviews are overwhelmingly positive. There seems to be some issues with balance, but that shouldn't bother hardcore DC fans looking to live out their fantasy of Aquaman becoming the most powerful DC hero.