I think that Spider Man is cooler from a character standpoint. A scrawny kid that is granted power and responsibility through a good luck/bad luck accident. Very human inside with all of the insecurities and such.
Batman is a multi Billionaire that lost his parents and like his father and Spidey has a genius IQ. He beats everyone without using superpowers just by being the absolute best at every martial art and utilizing strategy. It's harder for me to relate to him, I'd use lethal force on the criminals if both my parents were brutally slain.
In a fight I'd go with Bats. Anybody that has a plan in place to take out Superman if need be is tough to beat. Too bad he'd clean up Gotham faster as it's mayor than as Batman.