My vote is for the Webslinger!
I'm a huge fan of the wall-crawler, but thats not why I voted for him ^_o
Both 'contestants' are at the head of their game, the Dark Knight has a physical strength that dominates many, many humans with agility to match. Batmans gadgets and wits are undoubtedly his strongest weapons, BUT he succeeds only where a weakness can be taken advantage of.
Spider-Man, even as an early mutated youth was capable of handling even the toughest super-villans, not to mention that Peter Parker is a genius in his own right (developing web-shooters and fluid is no easy task : i've tried
). Not only the obvious, but his agility is unparalleled in the Super-Hero universe, the ability to gain traction on any surface and the Ace: his Spider-Sense give him an inital advantage over any non-super-human foe.
Spidey can lift iirc a Car without help, he has been known to complete even greater feats when put under pressure (such as holding up a supporting beam of the Daily Bugle building when he was trapped beneath it - easilly weighing inxs of 20 cars). If a Spiders web was made to be the thickness of Spider-Mans it would be capable of replacing the support cables on the Golden Gates bridge, now, Spider-Mans webfluid isn't an exact replica of a Spiders and so it doesn't have as high a level of potency BUT it has been known to support great weights AND can be utilized in several ways (ie. a liquid form that has a high level of adehsion), but it can easily be used to restrain an enemy.
The Batman could quite easily sever a Web of Spidey's: this is pretty much certan since he designs his own Batarags for Melee combat as well as projectile use, but in a match of Strength and Speed Spider-Man would win - hands down.
Even in a battle of wits where the Batman utilized an aid to match their strengths - Spider-Man would win. The webslinger has shown extreme amounts of endurace in his heroic history, even taking a sustained beating from the Juggernaught. but with his wits, Spider-Senses and speed he would overpower and dominate the Dark Knight. Afterall, the Batman relies heavily on intimidation, striking from the dark; both of which do not effect the wall crawler, a) because he isnt' phazed by any enemy, he just jokes while thinking up a solution and b) he could sense an attack in the dark, effectivly fighting with his eyes closed.
Woa, and yeah, I'm a Spidey Fan-Boy, but I also love the Dark Knight...but Spidey wins as far as I'm concerned, no contest.