The difference between re-birth and re-incarnation is, that in the case of re-birth the person becomes a child and to gain a happy childhood the memory of the former life has to be swept out. Therefore we are told, that the Fathers of the Dwarves got the memory of their former lives only back later when they were grown up again.
A person that is re-incarnated, on the other hand, gets back his own body in the state before its destruction which had led to the end of its former life, with memory of its former life and all else. In my point of view there was one great difference, but Tolkien did never address this point: The Elves in Middle-Earth faded, but in Valinor they did not. Therefore, I believe, that the body created for the re-incarnation was an unfaded body, even if the Elve had before lived in Middle-Earth and its former body had already shown significant signs of fading. That might have been a further reason, why only very few re-incarnated Elves left Valinor.
The Elves had not eternal life. They had life as long as Middle-Earth was inhabitable. If they lost their body during that time they went to Mandos not afterwards. What happened to them after Middle-Earth was ended they did not know. For Men on the other hand (and for Dwarves also) there was a promise of an after life even beyond the point of the last battle and the destruction of Middle-Earth.
Is re-birth a gift? Is death to an unknown doom a gift? Is a live as long as the existence of Middle-Earth, with an unknown doom afterwards a gift?
Who shall envy whom? We hear that Elves and Men did envy each other at times. Why should it be other wise with Men and Dwarves or Dwarves and Elves? Who would not wish (at times at least) back to the happy day of childhood with no responsibility and the freshness of so many experiences?
Respectfully
Findegil
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