Both translations are in verse, but they handle line length and register differently. Alexander runs longer lines that follow the forward momentum of the Greek more closely, keeping compounds like "single-hoofed horses" and holding the vocative weight of addresses like "Son of Tydeus, Diomedes, delighting my heart." Jordan works in shorter, tighter lines with a contemporary register. In Book 6, Alexander gives "so a generation of men either grows, or it dies," a full clause with its own finality. Jordan gives "In like manner the stock of men survives," which cuts the antithesis but lands cleanly. Alexander's diction sits in a formal middle register, elevated but not archaic. Jordan's is more conversational, occasionally plain to the point of flatness. Alexander's stated priority is fidelity to Homer's phrasing, and she keeps the word order and epithets close to the Greek, including "silver-footed" Thetis and "gleaming-eyed" Athena in their expected positions. This produces the texture of a scholarly translation meant also for reading aloud. Jordan reorganizes lines for English readability, sometimes adding words the Greek does not have. In Book 9, Alexander has Achilles lay out both fates in two parallel clauses that mirror the Greek structure; Jordan inserts "My mother, the goddess Thetis, told me" as a full sentence at the start, giving the passage more narrative ease but reducing the rhetorical weight of the original's tight balance. A reader who wants the architecture of Homer's sentences will find it in Alexander; a reader who wants clear, fast narrative movement will find it in Jordan.
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.
Sing, goddess, of Peleus' son Achilles' anger,
ruinous, that caused the Greeks untold ordeals,
consigned to Hades countless valiant souls,
heroes, and left their bodies prey for dogs
or feast for vultures. Zeus's will was done
from when those two first quarreled and split apart,
the king, Agamemnon, and matchless Achilles.