Throwing in my two cents:
Wolverine has the clear upper hand in melee(?), durability, resilience, and regeneration and the adamantium skeleton being a bitch.
Spiderman has the clear upper hand in strength, speed, agility, tactics, and the spider-sense giving him precognition in combat.
This feels like a speed vs durability type of match-up.
In a battle to the death or on attrition, Spiderman is probably unable to kill him for the most part and it all comes down to whether Wolverine can get lucky enough to decapitate Tobey if his throat happened to be close enough to be on the receiving end of his claw's reach to get slit. Otherwise, it would be a pretty prolonged stalemate until one of them gets tired and throws their hands up in the air.
In a battle based on incapacitation under normal circumstances, I think Spidey definitely has Wolverine beat more often than not in the short term at least. But not without a bloody ass fight.