Pope writes in heroic couplets, the dominant English verse form of the early eighteenth century, which means every thought gets sealed into a pair of rhyming ten-syllable lines. The effect is formal and elevated: in Book 9, his Achilles says "Short is my date, but deathless my renown," a line that is polished and aphoristic. Fitzgerald works in looser, unrhymed lines of varying length, keeping closer to the forward momentum of Homeric Greek. His Achilles says "if I sail back to my own land my glory / fails," which is plain and direct. Pope's register throughout is consciously archaic and stately, full of inversions and poetic contractions. Fitzgerald's language is contemporary without being casual, and his lines can run long or cut short depending on dramatic pressure. Pope's priority is a readable English poem for his own era, and he openly adds rhetorical weight where Homer is spare. In Book 21, Homer gives Achilles a blunt, almost casual speech before the killing; Pope's version inflates it with rhetorical questions and a formal close. Fitzgerald follows the Greek more closely in tone, letting Achilles say "Come, friend, face your death, you too," which lands as cold and abrupt, which is what the Greek actually does. Pope gains grandeur and a certain pleasure in the sound of his own machinery. Fitzgerald gives the reader something closer to Homer's speed and emotional directness. The reader who wants a monument of English literature gets Pope; the reader who wants to follow the story gets Fitzgerald.
Achilles' wrath, to Greece the direful spring
Of woes unnumbered, heavenly goddess, sing!
That wrath which hurled to Pluto's gloomy reign
The souls of mighty chiefs untimely slain;
Whose limbs, unburied on the naked shore,
Devouring dogs and hungry vultures tore.
Since great Achilles and Atrides strove,
Such was the sovereign doom, and such the will of Jove!
Anger be now your song, immortal one,
Akhilleus' anger, doomed and ruinous,
that caused the Akhaians loss on bitter loss
and crowded brave souls into the undergloom,
leaving so many dead men—carrion
for dogs and birds; and the will of Zeus was done.