First the pure history:
The Banff areas do not get a lot of snow but preserve it very well. On average early March is close to the optimal time of year. There is not a lot of margin for error, so in low snow years there can be a lot of rocks the whole season.
Big Sky's Lone Peak also has coverage issues because it's so steep, and most of the skiing from it faces south. The latter situation can lead to ugly melt and refreezes in March. Admin experienced this in early March 2001. I was there 2 weeks later after a storm had refreshed the surface and the skiing was excellent.
Odds of big dumps and deep powder are not the greatest at either but more likely at Big Sky.
The start to this season is about average at Banff but one of the best ever at Big Sky. The Lone Peak runs Liberty Bowl and Marx opened at the end of November, which is almost unheard of. So this year I would lean to Big Sky. I will probably be there myself in late January for a couple of days.
One of the great potential attractions of Big Sky is the new combined ticket with Moonlight Basin, which may provide access to north-facing terrain from the top of Lone Peak. This is the first year so there are as yet unanswered questions: nature of the terrain, how often it will be open, etc. Potential is spectacular; if it's open don't think twice about the $78 price of the combined ticket.