Bridger is definitely great for the small town ski hill vibe. They have good terrain if you get a beacon and ski the ridge. Otherwise it is really fun for just cruising around. Park isn't great, but can be fun at times. As people have mentioned it can be PACKED. Locals swear by Bridger, and when it snows big there, good luck finding a parking spot if you get there past 9:00 am.
Big Sky has waaaay more terrain, and a good mix of steeps and cruiser runs. There is a bus that runs up and that is a benefit if you don't have a car or just want to save on gas. The park is much better at Big Sky and the lines get crazy only on holidays or super deep days.
So I would say if you like park, and want an overall bigger selection of terrain, and also have a little more dough, get a pass at big sky. Otherwise Bridger is a good value, and the ridge is really awesome when it snows, and the local vibe is really good. Enjoy Bozeman and MSU! Great places