On what level are they competing? Devastating power, costume design, popularity among forum members?
If it's who has the strongest power, Superman obviously wins. He was created at time when most heroes had one power, so by combining the powers of a lot of the most popular ones, the result was a sort of metahero... the super hero. Whenever it was convenient to do so, they gave him another power. Lots of heroes in DC are like this. Almost everyone flies, super speed is common, they're all extremely strong/durable, etc. But Superman is always the top of the heap.
Of course who would win in a fight is ultimately determined by who's writing.
Costume design and popularity are totally subjective, though I'll always favor Batman in both. Outside the campy 60s costume, he's has some of the better ones. He doesn't have a bright primary color scheme to appeal to young readers, he dresses down to help him fight at night.
I don't know who has the best reason for fighting crime. Spidey fights out of guilt for Ben and Gwen (Gwen Stacey, Spidey's girlfriend killed by the Goblin), Batman wants revenge he can't have, and Superman is all about power and control. Once comics started to mature, there were times when each of these heroes had the nobility of their motives questioned. Superman comes the closest to doing what is right because it's right, but his supreme power prevents him from being questioned... leading to views of him as a moral facist like in Kingdom Come.
In the end though, despite all the Spidey comics I have, my favorite is Batman. Here's some quotes from The Dark Knight Returns (set 10 years after Bats' retirement) that show why:
And another:
Which sums up why I like Batman. He's a goodguy (arguably) who scares Superman.