Umm... Logan wins. Spidey would have to completely destroy him to make sure he wouldn't just regenerate, and Spidey wouldn't have it in him to kill Logan. Also Logan is a complete beast and Spidey only has martial arts and improvisation and spider silk. Logan has zeh claws -.-
It's not a Death Battle, so no need to kill. Spidey has Spider-Sense and is faster, so Logan can't touch him easily (or not at all). And he's strong enough to lift a tank. Logan won't die, but he'll surely get knocked out after a very long fight.Oh, and he beat the X-Men one time (Secret Wars Saga). Don't underestimate Spidey, he's VERY tough. Not trying to offend you or anything, just pointing out some facts for knowledge and fun.