Most MSU students go to Bridger, its closer than Moonlight and has some advantages. Which mountain you like best is really just personal preference. Bridger has some of the coolest/ hardest inbounds terrain in the US if you have a beacon, but most of it is hard to get to and most people who move here from the East or aren't use to skiing side-country and difficult route finding never get close to most of it. On the other hand Bridger's lower mountain is limited and shelfy, all the easy to get to areas get skied off early, and the slushmans line can be bad (BUT no worse than the tram line on a pow day at BS) and the park isn't very impressive. BS has a better park, is a lot bigger, ,and has more vertical, but there's not as much variety of terrain. The harder stuff: upper mountain (tram), areas off of Challenger, and the AZ chutes are all pretty much the same; steep, usually chutes, a couple of drops, usually chakey and windblown, and the landings always have pepper rocks. The rest of the mountain is pine tree skiing with the occasional cliff and the park. I haven't skied Moonlight, but the drive is long enough that it can be hard to go up before or after class.
Big sky gets more constant snow but Bridger goes off bigger. I've skied bridger the last two years but I'll probably get a big sky pass next year just to ski something different.