Never understood why they compare the two other than the fact that they're both really popular IPs with "Star" in their names, Star Trek is some hardcore Science Fiction and Star Wars is Science Fantasy, it's different.
But anyway, since i like Science Fantasy more than Science Fiction and because in my childhood I was more close to Star Wars, I choose... well, Star Wars.
It's funny, if you asked me this back in the 90's when Star Trek TNG was airing I would have said Star Trek hands down. Particularly I used to love all the technobabble. Oddly enough I learned alot of scientific concepts from that show. Since then we got the new Star Wars movies (particularly Episode 3 which was the best Star Wars movie to date), the Star Wars Clone Wars TV series, and Star Wars Knight of the Old Republic and other misc Staw Wars based video games, etc. Star Trek simply hasn't been able to keep up with Star Wars. That's why I picked I like both although I lean towards Star Wars right now. JJ Abrams Star Trek is eye candy, but it leaves out the science in science fiction which pisses me off because that's what I loved about Star Trek.
Although my name/avatar/persona is based off of my favorite Star Wars chracter, and I've always liked Star Wars a bit moreso than Star Trek, I honestly voted "both." The reason is that even w/ that tiny bit of favoritism of "Wars" over "Trek" I've never been one to bash one over the other and always gladly take anything from either franchise that I can get.
Star Trek is a show detailing Sciencetific advancements and their effects on Humanity. Not to mention offering a vision if a near-Utopian human society.
Star Wars is LOTR in space.
Star Trek wins.
Technically it's a metaphor reflecting the nature of politics and spirituality in society.
Historically, it can be compared to how Julius Caesar destroyed the Roman Republic into the Roman Empire, but it also seems to be a modern day cautionary tale warning of how history could repeat itself (i.e. George W. Bush's Presidency, etc.).
Spiritually it deals with positive and negative aspects of the nature of spirituality in relation to chi and duality.
Star Wars isn't always as intellectually satisfying as the Gene Roddenberry run portions of Star Trek, but it has it's moments.