Spiderman, he has taken on Quicksilver, a man of light, dodged multiple lasers, his strength is enough to knock Lee cold from one hit, he has taken hits form Hulk as well, Spiderman is also much stornger and can probably trick Lee into getting trapped in a spider web he made. He has also tanked hits and blast from iron man as well as being able to make him immobile, and keeping up with him (Although Iron man did troll Peter in one fo their fights :p) The main debate here is if Peter can tag Lee, his best feats are in his fight with Gaara way back Pre-Timeskip, we have not seen much from him now, if this were Guy it would be a totaly different story. Since it is Lee however, I stand by Spiderman being able to one-shot lee, being smarter, more agile, and arguably being able to keep up with his speed, this guy was albe to dodge lighting before, so I see no reason he can't dodge Lee, even with gates, he can arguably take him out before he activates it anyway. Not to mention Peter has knowledge on Lee and in the past we has seen Peter put his knowledge to good use, don't get me wrong, he is no Batman, Tony Stark, or Reed Richards, but he is pretty darn smart umong a lot of the Marvel U, Lee however has not shown very much intelligence with prep, I mean Sakura was able to trick him and Knock him, Kiba, and Sai out with a basic ninja tool, I see no reason Spiderman can't immobolize Lee with a web ball, not to mention Lee starts in base form, meaning Weights on anyway. Spiderman is definatly gonna have the advantage at the start.
Quicksilver was a jobber and really didn't pull off any Flash themed speed feats till regaining his powers. Him running circles around Spiderman, suffocating Spiderman, only to run into his arm isn't much of a feat since Quicksilver should have seen the thing move like a snail to him. The Hulk with any reasonable amount of force would insta splatter Spiderman with a punch, anyone in that range is completely out of Pete's league when they aren't jobbing to him.
Gaara pre-time skip was able to avoid the lotus when Lee literally blinked for a moment, imply Gaara had some insane speed even then. Gaara found himself however getting repeatedly strikes by the kid that was able to effortlessly hold these things in his hands:
Pre-time skip Lee regularly handicapped himself and ended up with a pretty bad beat down by the sound genin, Sakura abusing their trust and knocking the entire team out with gas(or whatever) wasn't much of a low end either. It's like trying to use the poison she made that Naruto nearly dies from right after is a low showing for him. Lee is still knocking down trees effortlessly in base and should, at the very least, have maintained some of that physical strength from Pre-shippuden, as with the speed. If he is getting immobolized by webbing he deserves to lose.
Spidey haves the edge on experience, and lately he haves also enhanced his hand to hand skills with Kung Fu, thus making him a much more deadly enemy. Rock Lee may be faster, but Spidey fighted faster enemies than him, and stronger enemies than him. Rock Lee will give an incredible fight, but Spidey haves the victory on the long term, since having longer versatility of moves, thanks to the webshooters, and the Spider-sense, he haves a great advantage over Rock Lee
I think the issue here is;
If they were bloodlusted, I can't see Spidey losing to Lee somehow. You know? He'd probably pull the First's head off the mountain and crush him or something.
In Character however, I think they'd end up having a bit of a brawl, to a standstill then give it up.
Also, again not to be obtuse here, but I don't really see Spidey EVER hitting Lee with webshooters so although I feel as though I have to give it to Spidey by default, I can't see how he would put Lee out for the count.