One of the biggest problems with Star Trek roleplaying is ... which Trek?
No, I don't mean which series necessarily, but what is your vision of Star Trek in general.
Take for example Starfleet Battles, a very influential vision of what Star Trek is all about -- in this game (first developed in the latter 70s) there is s strong emphasis on combat, especially space combat. Starfleet is essentially a military venture with a science overlay. In addition Larry Niven's Kzinti are involved and Klingons and Romulans (pre-movie era for the most part) are entirely enemy forces with no chance of alliances. This would require a set of rules based primarily, although not entirely, on starship combat. The game would be generally battle-intensive, even for on-the-ground dealings.
Then there is TNG, with its emphasis on talking matters out, diplomacy, and scientific problems. This would need an entirely different set of rules, with an emphasis on social interaction and scientific/engineering discovery.
The new movie could be almost anything -- the vision is still being formed, although it seems to be more action based than TNG; in some ways it feels like a throwback to TOS action ... yet the characters are still rough, unpolished, even unprepared.
So when deciding on a system, what kind of game are you playing? If it is personal-combat-oriented, go for some version of D&D; that would be as good as anything. Traveller might work better for a set of starship combat rules. For the more social aspects, you might be better served by a variant on World of Darkness or something like FUDGE or FATE or other more "freeform" rules.
Anyway, a few thoughts on the topic...