I think Spider-Man would have the slight edge because most of Batmans powers come from gadgets like his batarang etc. Now Spider_man has his spider sense so he could dodge all of the gadgets Batman could throw and since Batman doesnt believe in killing there is no chance he would use a can of Raid. (^_^)
This is a toughy. Batman has better "owers" but spider-man would defeat him in fisticuffs. My opinion is simple: spider-man beat the Hulk, and we all know that Hulk strongest one there is. So spider-man could defeat the lowly batman.