I've just come across this thread, so I'll add a few thoughts.
It’s interesting for me to reflect on what I find in the LOTR that I do not find elsewhere, or at least not in one book.
Multidimensional characters.
Gripping saga
Spiritual overtones
A truly epic sense of history (particularly true for me since I recently read the Silmarillion)
Coherent languages
Poetry, Songs, Myths, Legends
Perhaps most important is Tolkien's self-created term “Eucatastrophe”, “the sudden happy turn in a story which pierces you with a joy that brings tears.”
In my recent read of LOTR much to my surprise I experienced this several times, and it's seldom that I've experienced this in reading other authors.