I’ve been to all three (and fernie, silver star, Kicking Horse, lake louise, sunshine and even Cypress/Grouse in Vanc).
Banff – quite a cool town (little expensive- not too busy except at weekends), terrain excellent, lots of steep and deep, lifts fine. Other options in the area are Lake Louise and Sunshine, if you are in Banff you could easily combine from there. Lake louise is very windy on top even when its not windy. That’s great though cos its scares away all the skiers, so can be loads of stashes of wind blown powder there.
Big White is twinned with Silver star. Seems to be more life in Big White, the powder there is fantastic if you hit it right, the grooming is second to none and the place is completely dead most of the time as it’s a resort you have to travel to. Not too many locals. You can get a helicopter over to silver star for the day, it has an amazing back country section with tons and tons of black runs, completely empty, which are epic if you are into that.
Whistler is whistler, it can be the best place ever or the worst place ever. Completely depends on the snow, its always busy but you can find some peace out in seventh heaven or on the backside of whistler (involves a small hike). If it dumps which it can regularly do there, its unreal because the lifts are very very quick and there is plenty of places for solitude.
The best thing about Canada is the deals you can get. They are great at combining ski passes, accommodation at heavily discounted prices. Keep your eye on their websites.
Kicking horse, if you like the really steep stuff is epic. If I was you, I would definitely get a car for the three weeks and travel around that way. Sometimes there can be tons of snow in Fernie, yet none in Banff, its strange that way. The forecasts are excellent so you will know where to head. The resorts you have name are all big resorts and quite similar I suppose. All very well run, if you wanted something really different try fernie, red mountain or if you are really hardcore, head to Mt.Baker in Washington state about 90 minutes from Vancouver. They have the world record snowfall and the world famous banked slalom. Its mecca for snowboarders as the terrain is bananas.
Enjoy…..