Chapman writes in rhyming couplets with long, loose lines that push well past ten syllables. His Book 1 opening, "Achilles' baneful wrath resound, O Goddess, that impos'd / Infinite sorrows on the Greeks," keeps the invocation but reshapes it around the demands of rhyme, which forces compression in some places and padding in others. The register is archaic throughout: "ev'n I," "thy spirits," "chang'd." Alexander writes in unrhymed verse with lines that track the Greek sentence structure more closely. Her opening gives "Wrath, sing, goddess, of the ruinous wrath of Peleus' son Achilles," keeping the repeated word "wrath" that mirrors Homer's doubled emphasis on μῆνιν. Her diction is formal without being antique. Chapman was writing for Elizabethan performance and literary prestige. His Book 21 passage, "Die, die, my friend," has stage energy: it accelerates, it declaims. What it cuts is precision. Achilles' observation about his own beauty and mortality in the Greek is rendered as a rhetorical flourish rather than a plain statement. Alexander gives "Do you not see how magnificent and mighty I am," which is closer to the Greek's flat self-description. Her translation holds to the sentence-by-sentence logic of the original, including particles and connectives that Chapman freely drops. Chapman gains momentum and sound. Alexander keeps the argument legible. In the leaves passage from Book 6, Chapman adds "deserves no question" with no equivalent in the Greek; Alexander does not.
Achilles' baneful wrath resound, O Goddess, that impos'd
Infinite sorrows on the Greeks, and many brave souls loos'd
From breasts heroic; sent them far to that invisible cave
That no light comforts; and their limbs to dogs and vultures gave:
To all which Jove's will gave effect; from whom first strife begun
Betwixt Atrides, king of men, and Thetis' godlike son.
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.