Bridger is just a different vibe from bigsky/moonlight. Its a small ski town ski area with amazing terrain. Big Sky and Moonlight have a resort feel. Both big sky and moonlight have great advanced freeride terrain, the tram at big sky is all time. Drops you off at 11,000ft with nearly 4000ft vert pow runs. The park at moonlight is best, lots of features but only a jump or two. Big Sky has a decent park and usually a couple nice jumps.
At bridger a shovel, probe, partner are not required anymore just a transceiver and you can rent them in a couple places in town. the beacon rule and mandatory hike are there to keep unknowing people from getting in over their head. The steeps at big sky and moonlight are straight chutes, the ridge terrain at bridger is a maze of cliff bands. It requires scouting lines from below and putting your self in the right place once hiking to it (their is a guide book but not really worth it for a day). The lift served terrain at bridger is lots of fun too, more area to ride between the runs. The trees and underbrush and gullies keep you on the runs at ML. BS is just huge but i always feel the terrain is missing something.
My opinion is BS and ML are huge, and you could easily spend a week and not see it all. If you want much of a bar scene than its worth a trip to bozeman, and if your in bozeman you might as well ride bridger for a day. A day ticket at bridger is 48 vs 75 at bs and 65 at ml. Watch the weather storms hit the areas differently. In 2004 bridger got 76in of snow in 24 hrs and big sky got 7 in.