2. Is a terrible, terrible, terrible spite. Spider-Man stomps so hard.
1. Hulk for sure. Spider-Man would be able to dodge for a while and probably also escape in the end, but winning? I don't see that happening. He could come up with some fancy ass invention and kill Hulk somehow, but that would be hugely out of character for Spider-Man.
When he told Mary Jane, that he could kill the Hulk, then maybe he had in mind that he could suffocate Hulk, the same way he was threatening Kingpin, but I don't see that being the ultimate way to defeat the Hulk. Even if Spider-Man manages to put a good amount of web into Hulk's throat, it would not change the fact that Hulk could simply jump away.
One leap of Hulk and Spider-Man would need minutes, maybe even hours to catch up. Hulk can hold his breath for over 6 hours and people say that he can even evolve past the need to breath. Even if he can't, he can hold the breath for sure and 6 hours would be more then enough for the web to disappear.
Of course, we're talking about the Savage Hulk in this instance, who would probably not use his brain, jump away and camp the webbing out, but continue attacking Spider-Man, losing breath, so that he might even lose this one by suffocating.