Fordim,
An interesting question, but I think it's that word "better" that we are all tripping over.
If you had asked for a discussion of what I had gathered from the book--either intellectually or emotionally, I would probably be able to speak to that. Even then, there wouldn't be one answer set in stone, but a variety of responses. I've found that as my life goes forward, my situation changes and my response to various pieces of literature also changes. What I took from LotR at age 17, or age 35, is not identical to what I see there today. I am left with differing images and impressions, and find myself constantly noticing new things.
"Better" implies an overall assessment of myself as a person that I simply can't make. The closest I can come is to say that, without LotR, certain aspects of my life
might have been different. It was one of a small group of books that led me forward on a particular path: towards an interest in medieval literature and thought, towards living in Great Britain for a number of years and the eventual pursuit of several academic degrees, and, more recently, to take up writing again. At other times, I found the book gave me "nourishment" of spirit in particular junctures of life when things were not going well.
But as to whether I am a "better" person, I have no idea. Perhaps if I hadn't been chasing after faerie, I would have become a world renown medical doctor and discovered a cure for some deadly disease

. Seriously, I will leave such a broad assessment to the wisdom of providence.
Strangely, I find myself turning this question inside out. Was Frodo Baggins a "better" Hobbit because he became the Ringbearer? After all he had a series of amazing encounters with creatures of all kinds and learned many new things (just as we do from reading the books), but was he really a "better" Hobbit at the end of the tale? I don't think I can answer this, any more than I can answer the question in relation to myself. There are too many vagaries in both situations to come up with a sensible answer, I fear.