I have been cat skiing and heli-skiing.
Hands down, heli-skiing is much better, and worth the price.
Snowcats are slow. It's an inefficient way to get around the mountain. You'd get more vertical at a resort with fast chairlifts. You're also limited in terms of the terrain you can access, so if conditions are bad in one area, it's time-consuming to get to another. If you're lucky, you get some good turns, but you spend most of your time sitting in the cat, which is boring. The ride is pretty bumpy, so if you're prone to motion sickness, be aware of that.
With heli-skiing, the fun begins the moment you lift off. The helicopter takes off vertically and smoothly, then swoops around. It's unlike anything I've ever experienced in an airplane. The views of the mountains are breathtaking. My first time up, I joked, "Forget the skiing, I just want to ride in the helicopter."
A helicopter's preferred landing spot is at the top of a steep ridge, so that the passengers exit on one side of the ridge and the tail rotor (the most dangerous part of the helicopter) is on the other. Depending on the steepness of the ridge, sometimes you have to jump down - into powder, hopefully. So that part is pretty exciting as well. Then you have to crouch down and hang onto your gear, so the helicopter doesn't blow you or your stuff away as it takes off.
As for the skiing, for both heli and cat, I'd say that to really enjoy yourself, you need to have experience skiing off-piste at your local resort for at least a season. Although the guides do try to keep things within clients' ability level, there's no escaping the fact that it's a guided backcountry experience rather than a controlled resort, and conditions can vary. Sometimes you have to deal with ice, steep slopes, rock chutes, etc., in between the powder runs.
At the end of your run, the heli picks you up, and swoops off to the next ridge. The ride up takes maybe a minute or two, and it's fun.
I think cat skiing makes sense as heli-backup in a remote Alaskan lodge, for instance. Helicopters will only fly on bluebird days, for safety reasons. Otherwise the the most reasonable heli-backup is a resort.