I can only speak of Banff and Big Mountain having spent time at both.
My choice would be hands down Banff. You will have great conditions in
and around Banff during that time period and might have fewer people,
though I don't know when the Canadian school spring breaks are.
Sunshine and Lake Louise have a lot to offer and each of you can find
some fun terrain to explore, from cruisers to the challenging. Spend
time at both and see which you prefer (we like Sunshine). Sunshine has
three separate mountains, be sure to explore each. A car for Banff is
nice to have though not completely necessary (there are ski busses) but
having a car is more convenient. Inns of Banff is quite nice with a
large outdoor hot tub (almost pool) but is on the far end of town making
for a 15-20 minute walk to the downtown area (shops and restaurants).
The Canadian Rockies are beautiful summer or winter and try to do a
little sightseeing.
Have fun.