I have been to Big Sky two times:
1. Last year, mid Feb. great snow, no lift lines.
2. This year, spring break (March 26-29). Icy, windpacked, and terrible crowds. The mountain was very busy, but I think it was unusual for several reasons. Highwinds shut down many of the lifts, concentrating skiers on the Swift Current. Also, many skiers were inexperienced and clogged lifts that served groomed terrain. When Challenger was open it was not busy at all, but the good snow was very hard to find.
Overall, I think Big Sky is a great place, but too many people ( I could be included in this) are "finding out" about it and making it like other resorts. Still, lines only form on the base quads and the tram, and only during the peak weeks of the year. The snow we had this March was unusualy bad so don't worry about the month. I heard it is very often good well into April I rate it very highly.
Copper is great, (it is where I learned to ski), but the American Eagle and Flyer do get very crowded. Especially as it is turned into more and more of a resort town
. To get away though, just drop into resolution bowl.