There are some differences . . .
The most noted being, Mammoth Mt. owns the land the resort is on, MOST (not all, but most) resorts just lease the land from the forest service, so if you don't own the land, you can't make decisions about what areas are open, when they are open, and what kind of trails you can build.
In the case of Mammoth, they can do anything they want, because its their land. I have riden at Big Bear, and I found it to be "dual-crown downhill bike/full body armor" riding. Trail bikes are ok, but you'd have more fun on a downhill machine. Just my opinion.
I've skied at northstar, but not bikes, so I can't comment on that one. Mammoth is a blast, trails for everyone, stuff your grandmother could do on a comfort bike, trails that are fun on a trail bike and bommer downhill trails, it ain't the north shore, but I hear that they are puting in some stunt stuff.
It's the mountains, so if you don't like the weather, just hang out for about ten minutes, it will change!
Hot, cold, windy, cloudy at top and sunny at bottom, rain in the afternoon and everything in between.
Cheers, its a very fun place to ride.