I would say the LOTR books are better then the Matrix, but as movies I think the Matrix comes out on top.
Of course, if I hadn't read the books after seeing the Fellowship of the Ring my opinion might be different because I wouldn't know how much was changed/left out. My opinion of the first movie went down quite a bit after I read the book. I still like it, but the characters and the story in the movie just aren't as...awe-inspriring I guess. For instance Gimli in the books is a very noble character, while in the movies it seems he's mainly a souce of "comic relief".