Both translations are in verse, but they handle line length and register differently. Mitchell's lines are longer and more conversational: "The rage of Achilles—sing it now, goddess, sing through me" moves at a modern spoken rhythm, and his diction stays close to plain contemporary English throughout. Reck's lines are shorter and more compressed. In the leaves passage (Book 6), Mitchell expands to five lines where Reck uses four, and Reck's "wind spins them to the ground" against Mitchell's "the wind scatters one year's leaves on the ground" shows the contrast clearly. In Book 21, Mitchell writes "why all this moaning about it" and Reck writes "why whimper," one conversational and the other blunt. Neither translation reaches for archaic diction; both stay in a modern register, though Reck's is tighter and sometimes more abrupt. Mitchell tends to prioritize readability and forward movement. He occasionally adds words or lines that are not in the Greek: Book 1 ends his excerpt after line 7, leaving out the Apollo material, and his Athena speech in Book 5 opens mid-exchange, cutting the earlier part of the passage. The result reads cleanly but some Greek content is dropped. Reck stays closer to the Greek's line count and keeps more of its original elements, including "silverfoot Thetis" in Book 9 (Mitchell gives simply "Thetis") and Athena's green eyes in Book 5. Reck's compression occasionally produces awkward syntax, as in "live in decent obscurity." Mitchell avoids those rough spots but achieves the smoothness partly by adding or removing material.
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.
Sing, Goddess, Achilles' maniac rage:
ruinous thing! it roused a thousand sorrows
and hurled many souls of mighty warriors
to Hades, made their bodies food for dogs
and carrion birds—as Zeus's will foredoomed—
from the time relentless strife came between
Atreus' son, a king, and brave Achilles.