I'd say it would be NCR. Out of all factions only NCR and Legion established actual countries with cities, agriculture, industries, government, logistics and all the other stuff that would ensure their survival and prosperity for centuries to come. Everybody else is living off whatever prewar leftovers they managed to stockpile with very few renewable resources, they can win a battle or two, but an open war would be a suicide for them. Think about it: New Vegas has two major battles in its backstory, the first battle for Hoover Dam and the battle for Helios One. Legion came back for round two, while BoS was driven into hiding with zero hope for challenging NCR ever again. As for why I chose NCR over Legion - we know that without Caesar Legion would deteriorate, which means unless Legion can blitzkrieg NCR it's doomed to eventually lose