“Death is their fate, the gift of Ilúvatar, which as Time wears even the Powers shall envy.”
We call Men and Elves the Children of Ilúvatar. The Ainur did not fully understand the theme which resulted in their creation. That is to say, the Music of the Ainur imagined Men and Elves, but it wasn’t the Ainur who imagined them. It was Eru Himself who brought them into existence.
‘For the Children of Ilúvatar were conceived by him alone; and they came with the third theme, and were not in the theme which Ilúvatar propounded at the beginning, and none of the Ainur had part in their making. Therefore when they beheld them, the more did they love them, being things other than themselves, strange and free, wherein they saw the mind of Ilúvatar reflected anew, and learned yet a little more of his wisdom, which otherwise had been hidden even from the Ainur.’
The Silmarillion — Ainulindalë — The Music of the Ainur
There are many similarities between Elves and Men, especially in the Elder Days. Though awakening at different times, both Elves and Men originated in the east, marched for the west, and both left some of their kindred behind in the process. Both races were sundered, becoming smaller groups when they reached Beleriand. Eventually, they both left the shores of the continent, with some Elves reaching Valinor, and some Men making Númenor their home.
Those who made their way as far west as they could prospered compared to kin left in the east. Some of both groups were corrupted, and some returned east to found new realms in Middle-earth. Their creation and history are heavily tied together and they are not as different, even physically, as they may seem in adaptations of Tolkien’s work.
One major difference was the nature of their existence within the world itself. The first chapter of Quenta Silmarillion provides important information when it comes to life and death for Elves and Men…
“For an age Ilúvatar sat alone in thought. Then he spoke and said: ‘Behold I love the Earth, which shall be a mansion for the Quendi and the Atani! But the Quendi shall be the fairest of all earthly creatures…; and they shall have the greater bliss in this world. But to the Atani I will give a new gift.’ Therefore he willed that the hearts of Men should seek beyond the world and should find no rest therein; but they should have a virtue to shape their life…, beyond the Music of the Ainur, which is as fate to all things else.”
It is one with this gift of freedom that the children of Men dwell only a short space in the world alive, and are not bound to it, and depart soon whither the Elves know not. Whereas the Elves remain until the end of days…. For the Elves die not till the world dies, unless they are slain or waste in grief…. But the sons of Men die indeed, and leave the world; wherefore they are called the Guests, or the Strangers. Death is their fate, the gift of Ilúvatar, which as Time wears even the Powers shall envy. But Melkor has cast his shadow upon it, and confounded it with darkness, and brought forth evil out of good, and fear out of hope. Yet of old the Valar declared to the Elves in Valinor that Men shall join in the Second Music of the Ainur; whereas Ilúvatar has hot revealed what he purposes for the Elves after the World’s end….
The Silmarillion — Quenta Silmarillion — The History of the Silmarils — Chapter 1 — Of the Beginning of Days
Elves have their own gifts, as do Men. Elves do not share in the Gift of Men. Eru was not favouring one race over the other but was providing each with different gifts. Strangely enough, both sides have at times thought the other had the better deal. Elves can grow very weary amid the suffering they experience around them, and the decay and degradation of what they grow to love. Men have shorter lives and can become afraid of the unknown fate that awaits them. Elves know for certain what happens if they die.
The Númenóreans were corrupted by this so much, with the help of Sauron, that they attempted to take immortality by force from the Powers of the west. This was impossible, but Sauron cunningly took advantage of the seeds of doubt that his master Melkor had sown in the hearts of Men. Tolkien discusses the races and their weakness…
“In this mythological world the Elves and Men are in their incarnate forms kindred, but in the relation of their ‘spirits’ to the world in time represent different ‘experiments’, each of which has its own natural trend, and weakness. The Elves represent, as it were, the artistic, aesthetic, and purely scientific aspects of the Humane nature raised to a higher level than is actually seen in Men.
But the Elvish weakness is in these terms naturally to regret the past, and to become unwilling to face change: as if a man were to hate a very long book still going on, and wished to settle down in a favourite chapter.”
J.R.R. Tolkien — Letter 181
The original quote is directly referring to Men’s gift as the ultimate freedom; removal from the world itself. The Elves' fate is a Eucatastrophe; they are doomed to experience life over and over and suffer if the world suffers until it ends. Time will have its effect on Elves as well as the Ainur, who have existed since the beginning. Men’s removal from the world is a gift because they are not bound and have freedom. As long as the world endures, so do the powers and the Elves, whereas Men will depart it is said. This was always known as a gift until the corruption of Morgoth seeped its way into the hearts of Men, having many of them consider it a curse.