"Whereas to men he gave strange gifts..."
If memory serves me right, there are two strange gifts of men: to determine their own destiny, and to die. The elves, of course, are blessed with intelligence, immortality, and the ability to both live in the world and transcend it while they live in it. They are like a stained-glass window: their very nature, by its very nature, lets the light of the supernatural enter and be seen.
But there is one thing the elves lack. It is not obvious. In fact, it took me half an hour of wandering past stained glass windows to figure out what it was.
Consider an elf who performs an act of valor. It could be a great act. It could be a difficult act. It could be a humanly impossible act. But it does not make the elf a hero. Ironically, any act of heroism on the part of the elf has, of all things, an excuse: "He's an elf. Of course he could do that!"
In the War of the Ring, one of the most crisis-filled moments in LOTR history, when the continued existence of the Free Peoples of Middle-Earth seemed most impossible, the elves responded by flight (such as the elves of Rivendell who fled to the Undying Lands) or hopeless resistance (Galadriel). Even after victory, the elves are unable to save themselves: they flee or vanish, inevitably submitting to the destruction of the preserved things of the Rings.
In the LOTR universe, however, the actions of the human characters stand in marked contrast to this. Heroes arise out of the nowheres of the world: men like Turin Turambar, Elendil, or Aragorn come out of backward tribes, decaying nations, or defeated bloodlines. Their success is not based on their history or their culture (the elves' success is) and thus, rather than a linear devolution, it is cyclical, with not only fading kingdoms, but rising kingdoms. Unlike the elves, whose success, in the final analysis, depends on the action of the gods, the men are partially free even from the decrees of the gods (aka Valar), with Luthien (who becomes a woman) directly defying the Vala Mandos himself.
The elves are noble, great, helpless and lost. Men are dirty, fallen, and weak, but they have something the elves do not have: freedom to choose their good and evil fortunes.