Rieu writes in prose, and that choice shapes everything. His sentences run at conversational length, and the register stays close to mid-century plain English: "the anger of Achilles son of Peleus, that accursed anger." The phrasing is clear and moves fast. Wilson writes in verse, with lines that break and pause in ways prose cannot. Her opening, "Goddess, sing of the cataclysmic wrath," picks a single large word where Rieu spreads the weight across a clause. In the leaves passage (Book 6), Wilson's line breaks do real work: "The wind shakes some to earth. The forest sprouts / new foliage" gives each image its own breath. Rieu's version of the same passage reads as a compact paragraph, efficient but without the white space that slows a reader down. Rieu's stated aim was to make Homer readable to a general audience, and the passages show that. He cuts ceremony, moves the plot, and keeps the diction familiar. In Book 21, his Achilles says "Why make such a song about it?" which is colloquial to the point of anachronism, but it gets the dismissive tone across fast. Wilson stays closer to the Greek line structure and avoids that kind of idiom: "So die, my friend. Why are you so upset?" is plainer and less colorful but sits closer to what the Greek actually says. The cost for Rieu is occasional flatness in speeches where the original is formal. The cost for Wilson is that verse sometimes adds syllables the Greek does not have, as in her expanded Book 9 rendering of Achilles' two fates.
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.
Goddess, sing of the cataclysmic wrath
of great Achilles, son of Peleus,
which caused the Greeks immeasurable pain
and sent so many noble souls of heroes
to Hades, and made men the spoils of dogs,
a banquet for the birds, and so the plan
of Zeus unfolded—starting with the conflict
between great Agamemnon, lord of men,
and glorious Achilles.