This isn't even a contest. Spidey would spank Wolverine, not merely decisively, but embarassingly. He could stand toe-to-toe with Wolverine, and dip, dodge, and duck everything Wolverine threw at at him. Heck, he could stand there, perfectly still, and when Wolverine tried to attack, he's fast and skilled enough to just grab Wolverine's wrists with his hands, use his wall-crawling feat so Wolverine can't pull away, and then smack Wolverine with his own hands! (You know, the way older siblings torture younger one? "Stop hitting yourself, Logan!" *biff* "Stop hitting yourself!" *smack*). Wolverine cannot cut through Spidey's webbing, not in any reasonable time-frame, and certainly not if Spidey strings him up with his arms spread wide...no latitude to cut with, and not nearly enough strength to get it.
As far as Spidey's offensive odds, yes, Wolverine's Adamantium skeleton (assuming he has it) would protect him a lot. However, no amount of healing factor or metallic bones would protect his brain from rattling around inside his skull like a pinball machine after taking a couple of sharp punches from Spidey...and that's how people get K.O.'d in the real world, kids. Spidey would knock him out, at a moment of his choosing, and Wolverine would be powerless except to have some fanboys cursing the name of Spiderman on his behalf!
Spidey wins this, 10/10. Not even close.