This thread is limited to the
movie trilogies of Lord of the Rings and Star Wars, right? And by "Star Wars trilogy," we mean the original Star Wars trilogy, right?
In that case, Star Wars wins, hands-down. As movies, the Star Wars films have tighter production, more believable special effects (in my opinion), and showcase far better storytelling and character development. The Lord of the Rings films are absolutely fantastic, but have a tendency to take themselves too seriously and suffer from, in some cases, simply being overdone. This is not to say they are bad, but they simply cannot measure up to the humor, action, and very believable confrontations which permeate the Star Wars universe. Part of this may simply be due to the fact that there is
too much going on in the Lord of the Rings films; we are not called to focus on any one or two characters, but on the entire cast. Furthermore (and this is largely Tolkein's "fault"), Lord of the Rings simply meanders much too often; the entirety of The Two Towers is a digression from the main plot. Star Wars never digresses, because its plot is organic and divided over 3 movies (though arguably Return of the Jedi does feature several digressions--no wonder it is widely considered the weakest of the three).
On top of that, The Empire Strikes Back is easily one of the greatest movies ever made. It stands alone among the Star Wars movies as a really classy film, up there with The Godfather or Scorsese's Taxi Driver. Everything about it, from the lighting to the level of emotion each of the actors conveys, is really quite deep and well put together. While I do enjoy all of the Lord of the Rings films, I simply don't think any of them is orderly enough to compete with the perfectly-constructed narrative of Empire.
As far as action is concerned, Star Wars tops Lord of the Rings, if only because it is minimalist by comparison (that's funny to say, isn't it?). Both are economical enough, and in truth a greater proportion of time in Star Wars is probably taken up by shooting things; but Lord of the Rings sometimes just takes things ridiculously far. The battle in Return of the King was ferociously...boring. The sheer amount of density (something the disastrous Star Wars prequels also demonstrated) keeps the scenes from having the tightness and tension they should. Also, Empire contains what I consider to be one of the single greatest action scenes in movie history--the duel between Luke and Vader. This is great because it is, once again, focused on the two major characters, and elicits a level of tension and gravity most similar duels simply don't have. This is what I love about the Star Wars films. They're action movies, yes, but the action always contributes to the story and the characters.
Meanwhile, in Lord of the Rings, the action meanders often so that the films come to a standstill (as with the battle in Return of the King, as previously stated). However, I still believe the battle of Helm's Deep in The Two Towers is quite possibly the best large-scale battle ever filmed, and in spite of how messy it is, it manages to be quite powerful.
I sound like I've been bashing Lord of the Rings, don't I? well, to be fair, Star Wars sinks into utter silliness in Return of the Jedi, by far the weakest of the trilogy, and the characters lose their depth. It's telling that RotJ is a good film, but if we were to be completely honest with ourselves, the only real masterpiece among the Star Wars movies was Empire (oh, but what a masterpiece it was). The first Star Wars was about as good as popcorn films get, and Return of the Jedi was...good. Better than mediocre. Meanwhile, virtually all of the Lord of the Rings films are damn near masterpieces of filmmaking, and I would not change a thing about them. They adapt the books as properly as they could hope to.
So let's end with this. Both fantasy trilogies have their strengths and very few weaknesses.
I mean, come on, these guys are epic. They have lightsabers, telekinesis, telepathy, precognition, tele-friggin-kinesis, they can use the Force to do anything. Literally, anything. Anything they want. If I'm allowed to step outside the context of the movies for a second to point out the expanded universe, there are Jedi that can kill entire planets or make themselves immortal by constantly piecing together their utterly shattered bodies. It's the power to do anything. Look me in the eye and tell me you don't want the power to do anything.
Actually, I think this is a weakness, not a strength. To make all of the major characters so powerful actually cripples the plot; the quality of a story always involves working around one's limitations. I realize the Sith are a powerful foe, but part of what made the Jedi so mystical were characters like Yoda--even he had his limitations. Also, part of what made Star Wars so good in the first place was its Dune-like realism; remember all the raving about a "used future" reviewers were putting out back in the day? I have no interest in seeing something so far removed from any conception of physics that it divorces itself from being relatable to me. Fantasy films must walk that tightrope, and Star Wars and Lord of the Rings both did a good job of not taking things too far at first; unfortunately, the "used future" aspect has subsequently been sacrificed as far as Star Wars is concerned and replaced with stock fantasy "uber-power" childishness. I would only find any of this "cool" if it were on a heavy metal album cover.
Part of the problem with the prequel trilogy is that it really did make the Jedi virtually immortal, so that their deaths were completely arbitrary. Duels were ridiculous and had no emotional weight. One of the things I appreciated about both the Star Wars and Lord of the Rings trilogy was that the characters had very real limitations which were crippling at times, and even the force itself was not free from this. Zahn's Thrawn trilogy was so great in part because it limited force powers, even if the limitation is a bit contrived; it's sad to see that the rest of the Star Wars EU may as well be a bad 1,000-episode anime or video game in terms of how the characters use the force.
So while I do prefer Star Wars to Lord of the Rings, I'd actually take a few points off for the portrayal of the force. Fortunately, the original trilogy was not plagued by this ridiculously DBZ-esque use of "powers," or it would have boring as hell.