I think symmetrical is key for park skiing. I love the feel of symmetrical skis in the park, lower feeling swing weight and better balance on rails, not to mention big ass tails for lots of pop.
For anything else besides park and groomed runs though you would want asymmetrical just for the flotation aspect pretty much.. center mounted skis tend to tip-dive a lot in deeper snow unless they have insane amounts of rocker.
Or you could get a pair of skis like the kung fujas that have a symmetrical taper, which means the center of the sidecut is in the center of the ski, but it still has a wider tip than tail. This makes them carve and work great outside the park but still be able to center mount and ski switch really easy.
I have pipecleaners which are amazing park skis but feel a little funny if you are doing a lot of rails, they're bomb carving skis too. I also have some troublemakers mounted center and they're bomb park skis for rails and jumps and everything, hardly any swing weight. I had a pair of anthems until i blew them up too, and those were my favorite park ski by far. They could still make some wicked carves too, all you gotta do is keep facing down the hill and "screw" into the turn.