They're really different media and I don't typically compare them. I do tend to prefer Star Wars, but I'm not sure I can articulate why. I've always been a fan of epic stories.

One thing I might say along these lines is that the "more diversified" universe of Star Trek can actually become quite intimidating if you aren't already deep inside it. In order to enjoy Star Trek (real Star Trek, not the 2009 movie), you do need to have already bonded with the characters. I can watch an old episode of Next Generation and follow along because I watched them all when I was younger. But I could never sit down with my wife and do that - she'd have no clue why a Klingon has a wrinkled forehead or the backstory to Riker and Troy. 

Likewise, the breadth of Star Trek makes it difficult to really follow. Many people just don't have time to watch hundreds of episodes - much less the books, etc. I stopped watching Voyager after a while because I couldn't commit to watching it every week. Even now, when I haven't watched much Star Trek in a while, it seems intimidating to think about how I'd reengage with the Star Trek universe again. Would I watch the best episodes from each series? The movies (some of them weren't great)? I loved TOS and TNG and they formed many of my social and political views, but I don't think I'd get the same satisfaction from watching one or two episodes of Star Trek as I would one or two Star Wars movies.

Star Wars by contrast is somewhat more manageable. It's just 6 movies that are geared towards wider audiences. While there are some plot holes in the prequels, by and large most people can follow the films. If you want to expand beyond the movies, there is a HUGE expanded universe of books, comics, video games, etc. And, unlike the Star Trek novels, comics, etc, the Star Wars expanded universe is taken seriously by Star Wars fans - some of it has even been blessed as canon by Lucas. But, if you just want to experience Star Wars, you can limit your commitment to 6 films (or just the original 3 if you're a purist).

I don't mean to argue one is "better" than the other. I'm just positing that Star Trek might by its nature not be able to appeal to quite as wide an audience as Star Wars.

Yeah, I understand FreeDom4's view on Star Trek.  I have noticed lately DVD releases that just depict certain characters or episodes for Trek, such as The Captain's Log that has each TV captain choose his or her best episode as well as fan favorites.  Or there's another that only has Q episodes from The Next Generation and Voyager.  That might be the best way to catch up or dive in.  :)