I spent half of the 2011-2012 season in each place. Baker --> Big Sky. I moved to Big Sky on a whim... and I moved back to Bellingham/Baker after 6 months in Big Sky. I like deep snow. I don't like rocks. I love the PNW for many other reasons. Moving back here also had something to do with a certain boy that I'm probably gonna marry. But that's mostly irrelevant, except for the fact that if he didn't exist, I might live in Bozeman instead. So.... here's my 2cents on both spots. Hopefully this helps you out.
Baker's in bounds is tiny. The backcountry is endless, and often very dangerous due to the amount of snow we get on good years. It snowed 10 feet in a week or something stupid last winter. Also... storms like that are why Baker is fucking awesome. I've skied almost everywhere in the West and I've had seen deeper turns. Glacier, the closest town to Baker, is a crazy little town with barely any jobs and no cell service or gas station. Baker locals are crazy fucking hippies who like to go off into the woods and do mushrooms for days. Bellingham is pretty awesome for the most part, but it's an hour and half-ish to the mountain on a pow day. One of the emcees at the premiere of Jeremy Jones' Further the other night made a comment about how Baker is home to the true original hardcore these days. Like somebody else said, it's not a resort. It's a tiny ski area with a lot of backcountry for whatever you want to accomplish. I'm getting skins this year because I'm pretty bored with in bounds. Also, the premiere of Dream Factory was fucking lame compared to the Jeremy Jones movie. Almost everyone here snowboards, and there's not as much skier stoke as other places I've lived. Just something that bums me out.
Bozeman is fucking awesome. I miss it all the time. The people are rowdy, there's definitely a skier crowd in town, and it's noticeable. You'll have tons of people to ride with. Big Sky is gnarly. It's huge. If you get the Lone Peak Pass or whatever it's called, you get access to Moonlight and BS, and its the largest ski resort in the US, I believe. Endless terrain. I spent three months skiing there and I don't think I skied the same line twice. Even groomers. The trees are awesome. There's a bazillion smoke huts all over the mountain and patrol doesn't give a shit about that kinda thing. The snow is definitely lighter than the PNW, and it doesnt really stick. Locals make jokes about how all your skis are rock skis. Cause you'll hit rocks almost every day unless you're careful. The tram is sick. The A-Z chutes and the Headwaters  at Moonlight are pretty rad too. Lots of potential for scaring the shit out of yourself. You can see the Tetons from the top of the tram. 11,000 something feet up there. You won't be bored... but don't live in Big Sky unless you want to be bored and start doing coke to keep up with everyone else. 
If you have any specific questions, let me know. Also... Whistler and Jackson are far better than either of these. I'm actually  trying to move to Canada because its way sicker up North.
Sorry for the novel.