One of the reasons that FASA's Star Trek worked so well for me is that at the time all there was the original series, and a handful of movies. There was a sense of freedom and adventure in FASA's Star Trek that wasn't present for the Decipher and Last Unicorn version. The weight of Canon intimidates a lot of players and GMs. Perhaps unfairly.
It will say that both version has some pretty good writers creating their Narrator's guidebooks. Although the late John Ford did a kick ass job with FASA's Klingons. I was happy when Enterprise's solution to the differences between the TOS Klingons and the later Klingons was resolved using elements of Ford's solutions. (The TOS Klingons are the result of genetic manipulation of the Klingons by the Klingons themselves).
But since the positive reception of Abram's Star Trek now I see talk about refereeing Star Trek all over the place. Having seen the film a second time with my son, it is still a darn good film that was just as enjoyable to watch the second time as the first. It's most important aspect is that is restore the sense of adventure back to Star Trek and that anything can go. This make the setting a lot more appealing to referees and players.
Right now the only Star Trek RPG out there is Prime Directive by Amarillo Design Bureau. Which has it own unusual history. Luckily for fans of the new Star Trek it geared solely towards the Original Series. It comes in several flavors so you have your choice of system.
I think I will take mine in GURPS, loose leaf, three hole punched.