Butler's translation of the Iliad is more literal and traditional, while Mitchell's translation is more contemporary and accessible.
Sing, O goddess, the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down to Hades, and many a hero did it yield a prey to dogs and vultures, for so were the counsels of Jove fulfilled from the day on which the son of Atreus, king of men, and great Achilles, first fell out with one another.
The rage of Achilles—sing it now, goddess, sing through me
the deadly rage that caused the Achaeans such grief
and hurled down to Hades the souls of so many fighters,
leaving their naked flesh to be eaten by dogs
and carrion birds, as the will of Zeus was accomplished.
Begin at the time when bitter words first divided
that king of men, Agamemnon, and godlike Achilles.