I'd say they're equal as long as the anime doesn't give an indication that one of them is harder. Simple as that ;D
Being a Coordinator seems to be all about performing and variety regarding the battle-style, which, at first glance, seems to be a tad more than a Trainer must pay attention to in battle.
On the other hand though, I've never seen a judge cutting someone's points because they've used the same attack over and over again in the Anime (which happened a LOT of times), so the variety aspect is pretty unimportant in the end.
As for appeals...well, we've seen regular trainers (
) making it through the appeal round just fine. So the performances don't seem to be something that you have to practise often because they're very hard to think of to begin with, but rather because you want to perform different appeals in each Contest you enter, or because you're not a very creative/spontaneous person, so that you have to take your time to think of one.
As for difficulties that Trainers might have when entering a Contest for the first time is just that their points are cut even if an opponent merely dodges your attacks - something that is disregarded in Gym/League matches.
Depending on their experience, some Coordinators could have a problem with the possible length of a Gym/League Battle - your Pokémon ought to have a lot of stamina and patience, as there isn't a time limit set and Gym Battles could very well go on for more than an hour. There's also the fact that they have to realize that attacking prettily or dodging gracefully gets them nothing, but I don't think that would be much of a problem.
I highly doubt Coordinators would have trouble with the speed and force that Gym Battles are usually handled with either. After all, pretty moves don't necessarily have to be defensive or weak.