While the arguments for spidey are strong and I do like Spiderman much mroe as a character than Batman I'm going to tentatively go with Batman working under the assumption that Batman will always approach a fight from his own terms and create the conditions for his victory. Even then it'd be hard, but the way Batman fights generally gives him the edge.

Also, while both are extremely intelligent, I'd say Batman's much more experienced in the general area of fighting and tactics, which supports the above statement.

In a straight up match though Spidey would smack Batman around like nobody's business.