Another angle for SW vs ST was very deeply covered by a very interesting 1999 Salon article '"Star Wars" despots vs. "Star Trek" populists' by a sci-fi author David Brin.
As the title implies, Brin's evaluation is that Star Wars exemplifies the elite/heroic storytelling where select few decide for the unwashed masses what is good and bad for them.
Now, as far the difference between the fans (as per the question), this means that the fans of Star Wars are a lot more OK with the classical Homeric "big elite hero" worldview, as opposed to a more democratic (lower case 'd')/populist worldview of Star Trek fans.
Lest people think it's Brin's vivid imagination, here's the article quoting non other than Lucas himself:
Lucas defends his elitist view, telling the New York Times, "That's sort of why I say a benevolent despot is the ideal ruler. He can actually get things done. The idea that power corrupts is very true and it's a big human who can get past that."
In other words a royal figure or demigod, anointed by fate. (Like a billionaire moviemaker?)
To further quote Brin:
Regarding Star Wars:
Just what bill of goods are we being sold, between the frames?
Elites have an inherent right to arbitrary rule; common citizens needn't be consulted. They may only choose which elite to follow.
"Good" elites should act on their subjective whims, without evidence, argument or accountability.
Any amount of sin can be forgiven if you are important enough (think the "redemption" of Anakin at the end of ROTJ - DVK).
True leaders are born. It's genetic. The right to rule is inherited.
Justified human emotions can turn a good person evil.
Regarding Star Trek:
In "Star Trek," when authorities are defied, it is in order to overcome their mistakes or expose particular villains, not to portray all institutions as inherently hopeless. Good cops sometimes come when you call for help. Ironically, this image fosters useful criticism of authority, because it suggests that any of us can gain access to our flawed institutions, if we are determined enough -- and perhaps even fix them with fierce tools of citizenship.
By contrast, the oppressed "rebels" in "Star Wars" have no recourse in law or markets or science or democracy. They can only choose sides in a civil war between two wings of the same genetically superior royal family. They may not meddle or criticize. As Homeric spear-carriers, it's not their job.
 Please note the emphasis on lower case "d". You would probably find more in common - at least from a certain point of view - between the philosophical outlook by Star Trek fans, Tea Party people and Daily Kos crowd; as opposed to the views held by political elites of both parties that are closer to Star Wars creed (Kennedys and Bushes, anyone?). Attraction to populism exists on both ends of the political spectra, although right-ish libertarians would argue that left wing populism is a contradiction (or to put it more scientifically, and unstable equilibrium).