The Epilogue to Lord of the Rings, and a polished preliminary draft, were published alongside The Notion Club Papers in the ninth volume of The History of Middle Earth (1992) edited by Christopher Tolkien.
Considering that this was intended to be the final words of the LotR - and the end preferred by the author until an advanced stage of publication (perhaps early 1954) - the Epilogue has attracted surprisingly little interest and attention.
I think it makes a wonderful end to the story, and puts the book in a different and richer frame; but on the other hand the as-published LotR is perfection, so this is a minor quibble, really.
There are two kinds of reader of LotR: the one for whom 'Well, I'm back', he said are the final words - and those who, like myself, pause and take a deep breath (and wipe away a tear), then turn to the Appendices.
For the latter type of reader, the Epilogue is likely to be an even more satisfying end.
What are the advantages? In a nutshell the Epilogue emphasizes how the world has changed since the end of the Third Age and the departure of Elrond and Galadriel.
1. It brings the wheel full circle - the book began among the mundane affairs of the hobbits, and so it ends.
Very mundane in the sense of commencing with a rather stolid and unimaginative list of Questions and Answers about 'what happened next' to various major characters; as an example of the writing style of Samwise in The Red Book of Westmarch.
2. A scene between Sam and his eldest (and elven-fair) daughter Elanor follows - which includes one of the most beautiful, poignant and personal passages Tolkien ever (nearly) published:
“It was sad, Elanor,” said Sam, kissing her hair. “It was, but it isn't now. For why? Well, for one thing, Mr. Frodo has gone where the elven light isn't fading; and he deserved his reward. But I have had mine too. I have had lots of treasures. I am a very rich hobbit. And there is one other reason, which I shall whisper to you, a secret I have never told before to no one, nor put in the Book yet. Before he went Mr. Frodo said that my time maybe would come. I can wait. I think maybe we haven't said farewell for good. But I can wait. I have learned that much from the Elves at any rate. They are not so troubled about time. And so I think Celeborn is still happy among his trees, in an Elvish way. His time hasn't come, and he isn't tired of his land yet. When he is tired he can go.”
“And when you're tired, you will go Sam-dad. You will go to the Havens with the Elves. Then I shall go with you. I shall not part with you, like Arwen did with Elrond.”
“Maybe, maybe,” said Sam kissing her gently. “And maybe not. The choice of Luthien and Arwen comes to many Elanor, or something like it; and it isn't wise to choose before the time.”