In the fantasy-battle land, Batman would win, hands down. Why? He always has a plan. He has a plan for defeating every hero in the DC universe if they go evil. Including himself. Batman vs. Spiderman in Thunderdome? He probably has a plan. He's probably TRAINED for such an occasion ("plan for when I have no plan"). Never heard of Spiderman? Won't matter; he'd still have thought of a plan. The Marvel and DC universes have crossed over so many times throughout the years (there probably are several Batman vs. Spiderman comics), so even though they do not share continuity, he'd have heard of Spidey, and thus, have a plan ready.
Of course, this mostly applies to comic book Batman. Movie? Eh, tough to say, it's still early in his career. The only one Bats couldn't beat would be Deadpool, because he's impossible to plan against. Or to have a plan. Or to stick to a plan. Or sometimes even to spell "plan". You kinda have to wait for him to defeat himself, which isn't really Batman's style. Oh, and Squirrel Girl. NO ONE can defeat Squirrel Girl. Ever.
After reading more about the new movie, Andrew Garfield is Pete, good (loved him in Parnassus...loved Parnassus, actually). Martin Sheen as Uncle Ben, good. Rhys Ifans as the Lizard, good. Gwen Stacy in general, kinda meh. Stan Lee as Stan Lee, always good. J. Jonah Jameson cut from the movie...WHAT?!?!?! Pete as an emo rocker because "geeks aren't looked down upon"...you're losing me here.