Apples and oranges comparison, but personally it's the OT Star Wars. I'm more nostalgic for it, and though they were strongly influenced by Akira Kurosawa films, they were pretty dang original. LOTR is mostly original in its use of visual effects. The historical impact on film of Star Wars is also much stronger of course, including its impact on popular culture. As is its impact on the collectible world. Not sure this forum ever comes to exist without Star Wars.
But I love Lord of the Rings. The sentimentality is a bit much at times, and the ending of the last one drags on and on. But its the epitome of an epic fantasy story. And technically there's not much to fault.