While mages are powerful, what people don't consider is that the college mages aren't battlemages; they're just scholars. This being said I think Companions beat Mages, Mages beat Thieves, and Thieves beat Companions, like rock, paper, scissors. The College could hold out with wards, but they would be a terrible invading army. The Companions would dominate the battlefield and conquer like the original 500. But, like all things, it comes down to cold, hard, coin. The thieves guild has the most influence throughout Skyrim, they can buy off anyone to join their side and assassinate the competition.
Speaking of assassinate, why aren't the dark brotherhood included in this?. Wh, they only have 2-3 senior members anyway, oh, and an old woman's corpse... greeeaaaat...
Anyway, the college is so feared that the very townsfolk would fight them. These common folk would likely side with the companions, at least until they saw their more bestial nature. However, once again, all of the Yarls and movers and shakers would be under the thumb of the thieve's guild and it's coin; and that's what you need to win.