I'm not so sure the cosmic Spider-Man (Captain Universe) would win. We're talking about Superman, people. Not my favorite hero, far from it, but he deserves respect.
The problem with those cosmic beings is that their powers are always very vague : energy-beams, cosmic blasts, manipulating molecules, the ability to become much more stronger than you're actually are... that's all so... unclear, at least in my opinion.
It could be that the cosmic Spider-Man/Captain Universe will kick ass. But it also could very well be the other way around. Spider-Man can be cunning (Superman even more at times), but he's not used to these enormous powers. Superman is, from the day he was born (hm, kind of). And he uses them pretty well.
In the end, I think it comes down on who will be the smartest, and than Superman will be the last man standing.