Batman is awesome because he doesn't use brute strength to solve his problems. Oh sure, eventually he goes in and kicks some ass, but not before surveying the situation and choosing the best tactical option.
He constantly goes up agains people and creatures that are 100 times as powerful as him, and comes out on top.
It's just cooler than, say, Superman, because Superman has that whole "impervious to injury" trump card. Superman never has any awesome fights because he's either impervious and obviously going to win, or he's infected by Cryptonium and can't even move. Boring.