Mitchell writes in contemporary free verse with shorter, more flexible lines. His register is modern and colloquial: in Book 21 he gives Achilles "So courage, my friend" and "Why all this moaning about it," phrases that sound like natural speech. Alexander uses longer lines that stay closer to the Greek word order and syntax. Her Book 1 opening keeps "wrath" as the first word, matching Homer's "μῆνιν," while Mitchell restructures to "The rage of Achilles" and adds "sing through me," which has no direct equivalent in the Greek. Both are in verse, but Alexander's lines tend to run longer and feel more formal, while Mitchell's feel closer to spoken English. Alexander's translation keeps Greek epithets and formulaic phrases intact: "gleaming-eyed goddess," "single-hoofed horses," "lord of men." Mitchell often drops or replaces them. In Book 9, Alexander preserves the parallel structure of Achilles' two fates, holding the repeated "lost" in roughly the same syntactic position as the Greek. Mitchell simplifies the syntax and removes the second half of the contrast entirely, cutting the line about long life being peaceful rather than merely long. Alexander's approach serves readers who want to track Homer's compositional habits. Mitchell's removes friction for readers who want forward momentum in the story.
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.
Wrath—sing, goddess, of the ruinous wrath of Peleus' son Achilles,
that inflicted woes without number upon the Achaeans,
hurled forth to Hades many strong souls of warriors
and rendered their bodies prey for the dogs,
for all birds, and the will of Zeus was accomplished;
sing from when they two first stood in conflict—
Atreus' son, lord of men, and godlike Achilles.