I actually think Fellowship is by far the strongest film PJ has done in his career.
It is well paced (at least the theatrical version is) and tells its story in an epic, but economical way. TTT is a very entertaining action movie, but it does not have much of a beginning or ending and relies heavily on our love of the previous film and the conclusion of the following to the point where it cannot stand on its own. However, Helm's Deep is an epic sequence that does his bloated style perfectly.
ROTK while the one I may enjoy the most in some ways, shows even in its theatrical cut the problems that would come to haunt PJ's style. While Helm's Deep was epic and riveting, the even more stunning Battle for Gondor in ROTK is a good 15-20 minutes too long and goes on an absurd length of nearly an hour. Never mind the awkward way he ends it. I am not complaining about going back to the Shire, I am complaining that he intentionally has several fake-out endings which is just bizarre.
These indulgences which were peaking through ROTK's greatness became an albatross around King Kong's neck in which a simple popcorn story became a 3-hour chore to watch. And that has only broadened more until we got The Hobbit, which is a 9-hour film based on a book less than 300 pages long.
....So, in short, FOTR is the best one.
On an aside, however anyone feels about TDKR, at least it wasn't that odd Tolkien abomination we got in December. I think we can call it for the Nolan trilogy in that match-up right now. Just saying.