Star Trek: Jean-Luc Picard.
Okay, Picard is just The Man, and that's all there is to it. Awesome Shakespearean accent, awesome Patrick Stewart acting. I'm going to show my nerdiness when I quote Tasha Yar (after her DEATH), "A man with the heart of an adventurer and the soul of a poet." And may I add: never, ever whiny.
2. The Token Hotshot
Star Wars: Han Solo.
Okay, there's no denying that Han Solo is the coolest character in Star Wars, at least from my perspective. And Harrison Ford is generally always an entertaining actor. But Han? He is totally a self-absorbed mercenary at the beginning. He does redeem himself, fortunately... but still.
Star Trek: William Riker.

Will starts off the series as kind of a friendly jerk, but then he gets older, puts on some weight, grows a beard, and mellows out. He's all friendly and good-natured (and also a total womanizer but apparently that's okay because it's The Future), but constantly demonstrates that he is a Hotshot with Mad Leadership and Tactical Skills. He gets offered positions as captain on various starships like three billion times but decides to stay on the Enterprise, which is admittedly a little contrived, but what are you gonna do?
3. The Token Female Character
Star Wars: Leia.
Leia, like her brother, is all about Total Character Shift midway through. She goes from being a white-robed, weird-hairdo-ed damsel in distress ("Help me, Obi-Wan Kenobi!") to being kind of kickass, riding around on speeders and zapping storm troopers. A little weird, don't you think? Also-- bizarrely incestuous romantic gestures, anyone?
Star Trek: Beverly Crusher.
Dr. Crusher runs around sick bay, shattering gender boundaries left and right. She always makes the diagnosis (thanks to the handy-dandy tricorder thingy), and when it's a brand-new never-before-seen illness, she just figures out a cure all by herself. Also, there's some romantic tension with Picard thrown in for good measure, but no incestuous moments. Fortunately.
4. The Token African-American Character (hey, blame the times, not me.)
Star Wars: Lando Calrissian.
Forgive me if I misunderstand the plot nuances, but isn't Lando kind of a slimeball who betrays his "friends" and hands them over to the bad guys? Despite his inevitable subsequent redemption? Man. The dude even just looks kind of sleazy, doesn't he?
Star Trek: Geordi LaForge
Geordi, on the other hand, is never a slimeball. (In fact, none of the Enterprise crew is ever anything but totally honorable, dutiful, and caring. If that's what the future will be like, then I'm all about it.) He knows a ridiculous amount of crazy things about quantum physics and stuff, but is charmingly inept when it comes to relationships.
5. The Token Know-it-all Robot Character
Star Wars: C3PO
C3PO is annoying, and everyone knows it. For one thing, he may speak a lot of languages, but he doesn't know nearly as much as he thinks he does. Also, he's a total wuss. And far too shiny.
Star Trek: Data
Data, on the other hand, knows exactly the amount of information he thinks he does. And he's always doing heroic things like offering to use his own body to shield other crew members from electricity, fire, and who knows what else. And trying endearingly to be more human.
6. The Token Whiz Kid Character
Star Wars: R2D2

Okay, R2D2 isn't exactly a whiz "kid," but he (she? it?) serves the same function. And he is oddly appealing, and saves the day frequently, but.... wtf? Why can't he talk? Wouldn't it be easier to just program a robot to
talk than for everyone to apparently learn his "language" and translate his beeps and buzzes for the benefit of the audience?
Star Trek: Wesley Crusher

Wesley is almost unbearably geeky and naive for the first couple seasons, but he gets better as he gets older (and gets rid of that awful 80s rainbow-stripe sweater). And he has an IQ of like, 340.
7. The Token Scary Warrior-Type Character
Star Wars: Chewbacca
Again, what is up with the lack of dialogue? Obviously Chewie understands English, so why can't he speak it? I mean, seriously, how weird would it be if you had a friend from another country, and you both understood each other's languages, but you each insisted on carrying on your side of the conversation in your own native tongue?
Star Trek: Worf

Man, if you think the rest of the Enterprise crew is all about being honorable, they've got nothing on Worf. And when the other Klingons are mocking him for hanging out with humans? He just growls and takes it, because he's a freakin' Starfleet Officer, even though you know he would otherwise smash in their skulls. With his bare hands.
8. The Token Mystic Character
Star Wars: Yoda

I'm not dissing Yoda. But is there any particular
reason he has to talk that way?
Star Trek: Deanna Troi

Fine, she's an
empath, not really a mystic, but close enough. Admittedly, not as awesome as Yoda.... but definitely way hotter. I don't know exactly why she doesn't have to wear the Starfleet uniform like everyone else, but I suspect it has something to do with her rather impressive cleavage.
So there you have it. Not only evidence that Star Trek beats out Star Wars, but also evidence of the frightening magnitude of my geekiness. Be afraid, be very afraid.