It's been a while since I've watch a Stars Wars movie, but I'd say I'm kinda torn between the two, personally. I grew up on TNG, but we also used to watch syndicated reruns of the Shatner crew as well.
I really liked the first Star Trek movie. I bought it on DVD. The second one, we watched in in Imax. It wasn't horrible, but I didn't feel the need to own it and haven't watched it again since. I've watched the first a few times.
I'll definitely see this new Star Trek movie, but I think I'm currently more hyped about Star Wars. That said, I won't be out to see it on opening weekend. I'll do my best to avoid spoilers and catch it a bit further out (hopefully) to avoid the massive crowds.