Oh man, I saw Star Trek yesterday, and there were a load of proper trekkies in it. It was even funnier because they were really old, like 50, and laughed really loud at everyting Scotty said. Me and my mates were like WTF?!
Star Wars is a story that could be set in a variety of environments. But Star Trek is most true to the essence of science fiction - to explore strange new worlds, to help imagine what the future is going to look like on our present course (or what it could be if we improved as a species), and to put the characters in imaginative environments only possible in the scifi context in a way that illustrates a truth about the human condition.
While I don't agree with a lot of what ST says along that vein (Their utopian society is absurd imho), at least they try, and many times do very well. DS9 moved away from that vision in its later seasons, and the new ST movie doesn't have any of it, but TOS and TNG did it great.