I'd go to Snowbird. There is no Mineral Basin or Little Cloud at Alta. SB also has a more northern exposure which could be important if's warm, sunny and hasn't snowed for a while. Warm weather can play hell in late March, but maybe not.
Alta has the reputation of being "magical" as you say, why is that? In comparison to Snowbird.
"Skiing as it was? and should be"
1. Yes, the snowfall tends to be a little higher than Snowbird. (won't matter 12 hrs later)
2. A couple decades ago the lift tickets were cheaper than Snowbird
3. Snowboards not allowed, fine by me.
4. Old beat-up lodges (mostly not true anymore except for base lodge)
5. Not run by capitalist, profit-seekers like Snowbird, just saying
6 Alta was there first!!!!
7. Old beat-up lifts (gone! except for one)
8. Compared to SB - There are a bunch more places where you have to earn your turns(climb up!) and only get there by local knowledge. (all inbound). They ski out quick too unless you are in the line-up.
9. There is A LOT of History at Alta. Opened 1938 by famous Alf Engen. Now that's MAGICAL!!!!
Saying all that. I always ski a day at Alta on my trips. I like the place!!!