It's a bit of a hard question, because while Ceasar's Legion tends to favor weapons that seem crude even by the standards of a psuedo-Medieval fantasy setting (Just look at those machetes they carry.) they do have access to some more advanced weapons, like say, guns. Yeah... I'm pretty sure that Imperial Legion soldiers would be in for a nasty surprise when their enemies pull guns on them. And at least some members of Ceasar's Legion seem to use power fists and displacer gloves at all. On the other hand, the Imperial Legion comes from a world of magic and lizard people, and with magic, one can do all the things that people from Fallout can do with technology, and more. Sure, guns can kill people, but so can destruction magic, and despite what the gameplay mechanics would indicate, I'm sure restoration is more effective at healing in reality than stimpaks, and the legion seems to be against that sort of thing anyway. Magic also has other uses like teleportation, levitation (Even though those two spells were removed in Oblivion.) walking on water, and so on. Of course, magic isn't exactly something that every Imperial Legionary uses, but if the Imperials have battlemages in their midst, it might give them an edge in battle. But there's a bit more to the question of who wins and who loses than just who has better technology. The number of troops either side has would also need to be considered, as well as the tactical positions each side has, and even then, we must still consider the fact that the Imperial Legion is the military force of a continent-wide Empire that has existed for centuries, while Ceasar's Legion is a collection of conquered post apocalyptic tribes that has, at the of New Vegas, only been around for a reletively short time, and its territory is probably much smaller than Tamriel. This would have an effect on the resources available to each faction, I'd imagine. Even though I like the Imperial Legion better, that's really not grounds enough to say they would win. Admitably "Who would win" type discussions often boil down to popularity contests between the two sides, but if you really want to reach an accurate conclusion as to which side would have the advantage, if, by some chance, they actually fought.
All things considered, I can't really say for certain who would win, and it's really not relevant, unless you plan on writing an Elder Scrolls/Fallout crossover. Both organizations exist in completely different worlds, with very different cultures and technology, and even different laws of nature. Comparing the two is like comparing tigers and squids. Or perhaps it would be more accurate to replace squids with an alien lifeform native to a distant planet tha has never even seen tigers from a science-fiction universe of your choice.