Who would win in a fight between Superman and Batman?

The fight has already taken place, at the end of "Batman: The Dark Knight Returns" Batman uses a cloud of green Kryptonite gas to rob Superman of his powers, and had no trouble beating him up. Superman can win a fight... but Batman can plan a battle. There's a difference. Superman has called Batman the "most dangerous man alive".

There is a school of thought that says Superman will win as Superman is bulletproof and can lift a building, has heat vision and x-ray vision.

Broken down this theory states that:

Superman:
- Immune to everything but the stone of a single light-years away asteroid belt (formerly planet)
- Faster then a speeding bullet
- Able to leap tall building in a single bound
- Super strong
- Flight abilities

Batman:
- Rich
- Mostly bullet proof when in armor
- Has a car with a rocket in it

However this opinion misses out 2 key factors:
  1. Batman is the only person in the universe Superman is actually scared of including Zod, Doomsday and The Joker.
  2. Superman gave Batman Kryptonite specifically for the purpose of defeating him should the need ever arise.

it depends on which version of superman you are using, but also on whether batman has prep or not. It was stated in some comic that batman only carries kryptonite around with him if his is in metropolis, so in a chance meeting, superman will win.