Rieu writes in continuous prose, with no line breaks and no fixed rhythm. Mitchell writes in verse, with each line carrying a rough forward stress. The difference shows immediately in Book 1: Rieu opens "Anger — sing, goddess, the anger of Achilles," then folds the rest into flowing clauses, while Mitchell breaks the same material into seven lines, each ending on a word that holds slight weight ("me," "grief," "fighters"). Rieu's register is educated but plain, occasionally colloquial. In Book 21, he gives Achilles "Why make such a song about it?" Mitchell has "Why all this moaning about it?" Both are contemporary in diction, though Rieu reaches toward the conversational more readily and Mitchell stays a degree more formal. Rieu, writing in the postwar years for Penguin's paperback classics series, aimed at readers with no Greek, and his prose prioritizes ease of reading over any feeling of performance. He cuts the repeated epithets and formulaic phrases that slow verse, so the story moves quickly. Mitchell keeps more of Homer's structural repetition, as in the Book 5 exchange where Athena's full speech in verse lets the rhythm do some of the argumentative work. What Rieu gains in pace, he gives up in texture: the Greek is a poem, and prose removes the forward pressure that meter creates. Mitchell's verse restores some of that pressure, but his line lengths vary enough that the meter rarely feels strict. A reader who wants the story told directly will find Rieu easier to stay inside; a reader who wants something that feels composed will notice it more in Mitchell.
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.
The rage of Achilles—sing it now, goddess, sing through me
the deadly rage that caused the Achaeans such grief
and hurled down to Hades the souls of so many fighters,
leaving their naked flesh to be eaten by dogs
and carrion birds, as the will of Zeus was accomplished.
Begin at the time when bitter words first divided
that king of men, Agamemnon, and godlike Achilles.