When you think about it, a truly evil, ruthless Spider Man - let's say, one with the Punisher's motives and mentality - would be an absolutely brutal assassin. The combination of strength, speed, agility, intelligence, and virtual precognition would make him a devastating clandestine killing machine. If he knew pressure points, how to snap a neck, where to punch to paralyze or kill, he would absolute decimate people far stronger and tougher than him because he's a complete package that just comes together brutally. Villains are lucky he doesn't look at them like Frank Castle does, because it's hard to think up a better powerset for an outright killer than Spider Man has. I think somewhere deep down, for all of his self deprecating humour, Spidey actually realizes this, as he has gone on record saying that if the Hulk ever really went out of control, he would and could kill him, meaning he thinks he has that capability.
Wolverine is a pretty nasty and tough bugger but he's not really all that powerful. If an evil Spidey with that look in his eye wanted him dead, he'd find a way to put him down with ease - and the, through his genius level intellect, find a way to keep him down. Even if, as people have speculated, Wolverine is functionally immortal (horrible writing that doesn't reflect the established power levels of a few decades ago), he'd find himself waking up from having his head ripped off buried in the cement foundation of a new skyscraper.
