There's a shitload of arguments that can be made here. Personally, I'm sure big mtn is harder because even I can sorta ski park.
-A given trick may well be easier in the park then off a cliff or a bc booter. Also take into account that a park rat from MN wouldn't even make it to the booter/cliff alive and with enough speed.
-You have to get to the big mountain. Thats what keeps a lot of people from doing it, you don't just get off a lift and go.
-Big mountain skiing takes special skills. The ability to prevent or deal with avalanches, for example, isn't knowledge thats distributed widely across the country. I come from MN, and as sad as it is, I go out west to ski park, maybe a little bit of all mtn but only in bounds. Why? Because I don't want to die, I don't have the skills to take part in this type of skiing that so many claim is ten times better than park.
-Big mountain gear is an additional cost, not everybody wants to throw down the $$ it takes to get some skis that are 100+ at the waist, and the other little things that go along with leaving the resorts.
Now in terms of just the simple act of skiing, mechanics, muscles, etc, its a toss up. Raise somebody in open bowls, deep pow, steep cliffs, tight trees, etc. Now put that person on a rail and see what happens. My guess is that it'll probably be good for a few laughs. That not saying that person isn't in control of their skis, etc, but being able to do pow doesn't mean you can do rails or stalls, and park jumps (while they may come easier) aren't the same as booters. In the same way if you raise a person only doing park, their ability to actually ski goes in the shitter. Put that person at the top of some gnarly line and tell them to make it down. They will most likely die.
So you can ask who is the better "skier" and the answer is probably the big mountain skier. I'm a park rat, and I'll admit that my ability to ski, well, there isn't one anymore. Park skiing, particularly jibbing, is a whole new skill set that really won't help you when you go where the lift won't take you.