If you haven't seen the movie, I suggest you don't read this, but you have been warned!
So if you've seen the movie, I'm sure you've seen the fighting scene already. So if we look at the fight it's clear to say that Batman had the upper hand, but despite that he still had a tough time trying to bring the Man of Steel down to his level of strength. Batman had the advantage being able to set up all of his fancy gadgets, plus he got to pick the place to fight, so I must say he had the upper hand, but let's not forget the fact that it was hard to bring Superman down to his level of strength.
Let's talk about the real fight here, Batman's first few attacks were basically useless I would have to say, it only annoyed him. I think the fight really began to heat up when he shot Superman with the kyryptonite gas, and from that it weakened the Superman. He needed to fire these shots from time to time to weaken Superman, but in the end he had the kryptonite spear with him ready to kill Superman. If it wasn't for Lois Lane and Martha(Superman's mom), Superman could've been killed at that moment. So in conclusion Batman could've killed and beat Superman.
But let's take a look at another scenario. Superman with no doubt could actually beat Batman, if he was able to choose where to fight, decided to fight Batman without warning the Dark Knight, catching him by surprise, and by not letting him know that there would even be a fight. Then, obviously, Superman would win the fight, definitely no doubt there. Or is there?