This should be interesting since I think most of the people on this board either remember when Star Wars came out or were at least born right around that time. So some people may pick Star Wars for purely sentimental reasons. And Star Wars probably has a greater number of fanatics.
Personally I think Lord of the rings is a better triology (even though the third part hasn't been released yet). Honestly (and I know some people will rip me apart for saying this), even though I saw Star Wars when I was young when it first came out and thought it kicked ass at the time, now that I'm older I've come to see it as more of a marketing tool than a movie. The characters are wafer thin, the recycled plot was made even more generic by Lucas so it would have broader appeal, and the directing in all three is servicable at best. Lucas made, in essence, a generic revenge/adventure tale and dressed it up with a neato lightshow.
This makes it sound like I hate the movie, which I don't. But I do get the feeling more and more (especially now that the new ones have come out) that Lucas sold me a product way back when and convinced me that it was great entertainment, even art. Everything about the movie says "hey look how epic this is, look how emotional this is, look how cool this is" without ever providing the depth that makes movies epic, emotional, and, well, cool.
I guess I'm kinda pissed. I feel like I got ripped off way back when and I want my money back
(what was it like three bucks back then?).
That's why LOTR gets my vote. It may not be high art, but it's certainly great entertainment.
As for the poll there's a choice for those who don't want to pass judgment until the LOTR Trilogy is complete and I had to put a couple of choices in for the die hard fans.