You boys know that the chaps over at shoddycast had a whole video on this as to why the legion would make the NCR pay, but would ultimately lose right? It's a fun video, informative... And insightful, they crunch a shit ton of numbers and even talk about some of the issues brought up here.
My thoughts are pretty much theirs but, say Vegas and Mo-post fall, Cool beans, easy legion win right? No! Now they are in enemy territory, sure they could have sent scouts 'n' spies, but a few quick glances and notes are nothing compared to local knowledge, one of the reason my ancestors were such a thorn in side of the pale faces.. Er, pilgrims, If they knew the land better, where to hunt, where to hide, and where to watch is just as important as any other part of military planning. Its one of the reasons Laden was so hard to find for a while despite our over reliance on drones and other gizmos.
Now also, yeah sure, maybe the legion does outnumber the NCR, or maybe its the opposite, Point is there is a saying 'Even a mosquito can defeat an army'. So even if one side hugely outclasses the others in the number game, there are tons more variables that will fuddle those numbers. 'Murica 2.0's factories and ability to make more guns and ammo. As we see with the Boomers, Arty still lives in the world of Fallouts , so its very easy to assume that the NCR has some form of STC to make more, we see that they installed cannon on the damned dam for arties sake. Point to Murica cosplyin' NCR
Now for the legion, they are a very nimble army, not as agile as the NCR with trucks and plane, but they are, or at least can be, fairly lightweight. A man carrying a sword and a leather segmintata can surly run a lot longer than the same man lugging a 6-15 pound rifle, the ammunition for said rifle, body armor, pants, and what ever he might have in his pockets (trinkets from home, food, blah blah blah.) It's also stated they have a ton of slave power, so as long as they don't work them to death, it could be possible for the Romans to quickly extend their lines to follow the runners ahead of them, they also can be employed to build old style siege weapons (Really, a trebuchet is not that hard to build and you can find the blueprints for them online, Its a safe bet Ceaser read about them in books.) A point to the Sport equipment Romans.
In terms of which is better for the Mojave? All options really suck, you have the egotistical leaders of all the factions, House is self obsessed, Kimball is aloof, and Ceaser is... Um.. Yeah, dying, they are all pretty shitty leaders. I guess it boils down to 'Do you want to loose your head for saying this country sucks, or do you want to pay a 300 cap fine?' Bad example I am sure, I'm a very stoned Super mutant right now. Point is both sides could possible beat the other, both sides suck/rule for their own nifty cool reasons
Anyways, All in all, I put my money on the Vipers, they'll make a come back! (I kid of course, am I cool now?)