A quick historical question before I vote: were Rick Berman or Brannon Braga ever particularly popular?
This was my first thought when looking at the choices on the poll too. And I think it's a shame. I've never read anything about these two on the Internet that wasn't completely negative, and I'm getting really sick of it. All the mistakes he made in the later years of his Star Trek involvement cannot erase the fact that Berman was largely responsible for some of the best stuff to come out of "Star Trek: The Next Generation" in its golden years. Berman was to "Star Trek: The Next Generation" what Harve Bennett was to the original Star Trek movies and what Michael Piller was to "Deep Space Nine" - the primary creative force on the staff, through whom writers received the approval and guidance that lead to their finest output.
As for Braga, I know his record is much more spotty since he wrote a lot of lame "psychological" TNG episodes, but I can forgive him for a lot due to his co-writing "A Fistful of Datas", "Star Trek:First Contact", and "All Good Things". He also wrote one of the greatest and most original Star Trek episodes on his own ("Cause and Effect"), as well as some of my favourite guilty pleasures like "Frame of Mind" and "Parallels". To be fair, I suppose it's easier for me to not hate him than it is for others also because I really don't care at all about Voyager or Enterprise, so whatever negative influence he had on them doesn't affect my opinion of him.
To answer the main question of the thread, I'd say Frakes. I've actually thought about this from time to time over the years, and it really makes me sad to see what happened to his career. Like so many Star Trek actors, he was left in limbo as an actor after his tenure on Star Trek was over and that's not really tragic or surprising since it's so common, but I'm deeply disappointed by the trajectory of his career as a director. With "Star Trek: First Contact", he showed a lot of potential as a director. I think he developed his skills as a director over the years by directing episodes, and when it came time to prove his worth as the helmer of a big budget motion picture, he hit it out of the park.
Then he followed it up with "Insurrection", which was a flop, and then "Thunderbirds", which was an even bigger flop! After such an impressive debut, his directorial career totally tanked, and since the massive failure of "Thunderbirds", he's only ever managed to get the occassional direct-to-DVD or TV directing gigs. Now I'm not deluded enough to think he was ever destined to be one of the directing greats, but I believe he certainly deserved much better after the triumph of "First Contact". My love for that film makes me wish he'd had a lot more success in directing. I guess it's partially bad luck that the only scripts offered to him stunk, but it's also his fault, as he could have turned them down rather than kill all chances to helm a good movie again by accepting them. At least Leonard Nimoy had a hit outside of Star Trek ("Three Men and a Baby") and stopped directing by choice instead of losing the opportunity to be a major director because of a huge failure.