Both translations are in verse, but they handle line length and register very differently. Alexander keeps lines fairly close to the Greek's one-line-per-unit structure and holds to a relatively formal register throughout. Her opening, "Wrath, sing, goddess, of the ruinous wrath," stays elevated and controlled. Green's lines run longer and looser, and his register drops toward the colloquial at moments. In Book 5, where Athena describes Ares, Alexander has "this madman, created for evil, double-faced," while Green gives "this raving madman, a sick piece of work, a two-faced / liar." That phrase "sick piece of work" is openly contemporary speech. Green also adds exclamation-style phrasing ("Get up close, hit him") that reads more like a command shouted across a room than a divine pronouncement. Alexander prioritizes formal closeness to the Greek syntax and word order, which keeps the translation austere but occasionally produces lines that feel slightly compressed. Green prioritizes readability and spoken energy, which produces clearer narrative momentum but sometimes adds color the Greek does not contain. In Book 21, Alexander renders Achilles' taunt as "Come friend, you die too; why bewail this so?" Green gives "So, friend, you too must die: why then lament thus?" Both are close, but Green brackets the speech with explanatory framing elsewhere in the passage. Alexander's scholarly apparatus (notes, introduction) reflects her classical training; Green's marginal numbering and transliterated proper nouns (Hādēs, Arēs) show a similar concern for accuracy, aimed at readers who want to track the Greek closely.
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.
Wrath, goddess, sing of Achilles Pēleus's son's
calamitous wrath, which hit the Achaians with countless ills—
many the valiant souls it saw off down to Hādēs,
souls of heroes, their selves1 left as carrion for dogs
and all birds of prey, and the plan of Zeus was fulfilled
from the first moment those two men parted in fury,
Atreus's son, king of men, and the godlike Achilles.