If it's to kill, then it'll depend. In most cases, Spider-Man would lose, as he'd probably knock Logan on his ass, spare him, and then Logan would spring and stab the wall-crawler, Spidey having been too close to dodge fast enough. However, if we're talking enraged Peter, the one that almost murdered the Green Goblin with his bare hands, I'd still give the fight to Spider-Man. But Berserker Spidey is a rare sight.