Yeah you're gonna want a decently wide all-mountain ski at least, if it hasnt snowed in awhile there is no reason to rock really fat ski's. k2 Obsetheds or rossy s7's are pretty much the perfect ski for Snowbird if you're gonna look at renting something.
Honestly it's a lot more about the skier not the skis.
Everyone is talking like you NEED all mountain or big mountain skis to ski the bird or alta..
I skied there quite a bit on center mounted anthems and it was fine. If you're a decent skier you should be fine. Also, if your skis are fairly stiff you'll be good.
I must say though, I ride JJs now and they do better for sure.