Rieu writes in prose, with sentences that run at a conversational pace and a register pitched close to mid-twentieth-century educated English. The opening of Book 1 gives a clear example: Rieu writes "Anger — sing, goddess, the anger of Achilles" (the em dash aside), keeping the syntax plain and the vocabulary immediate. Jordan writes in unrhymed verse, with lines that hold roughly to a consistent length and a register slightly more formal. His Book 1 opening reads "Sing, goddess, of Peleus' son Achilles' anger, / ruinous, that caused the Greeks untold ordeals." The word "ruinous" carries more weight than Rieu's "accursed," and the line break after "anger" gives the word its own pause. Rieu's prose can move faster, but it also flattens the forward pulse that verse naturally builds. Rieu, writing in 1950 for Penguin Classics, aimed openly at the general reader who wanted a readable story. That shows in Book 21, where he cuts to "Yes, my friend, you die too. Why make such a song about it?" The phrase "make such a song about it" is colloquial and vivid, but it moves away from the Greek. Jordan stays closer to the line structure of the original and tends to keep more of what Homer names. In Book 9, where Achilles lays out his two fates, Jordan gives "I will die soon but my fame will never die," which tracks the Greek opposition closely. Rieu gives the same content in looser paraphrase. Jordan's verse form asks more of the reader; Rieu's prose asks less and gives back immediate narrative speed.
Anger — sing, goddess, the anger of Achilles son of Peleus, that accursed anger, which brought the Greeks endless sufferings and sent the mighty souls of many warriors to Hades, leaving their bodies as carrion for the dogs and a feast for the birds; and Zeus' purpose was fulfilled. It all began when Agamemnon lord of men and godlike Achilles quarrelled and parted.
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.