Despite my loyalty to the Russkie, I think War Machine would have better chances of winning, since he's just about as strong as Colossus is, but also has flight and various kinds of ranged weaponry on his side.
In my opinion, it all comes down to whether or not Spider-Man knows what Omega Red is capable of. If he doesn't know about the Death Spores and all that, Omega Red will have a good chance of killing him. If Spidey already knows about the Death Spores, then he'll be smart enough to avoid them and beat Omega Red.
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