Both translations are prose, but they read differently on the page. Rieu writes in longer, more controlled sentences with a contemporary register that stays close to standard English. His Book 1 opening, "Anger — sing, goddess, the anger of Achilles son of Peleus," places the key word first, mirrors the Greek word order, and then moves forward in clean declarative clauses. Rouse is shorter and more conversational, sometimes jarringly so. His Athena calls Ares "Mr. Facing-all-ways," and his Achilles tells Lycaon "Come, my friend, die too; why do you cry like that?" That second line has real bluntness. The leaves simile in Book 6 shows the register gap plainly: Rieu writes straight prose, Rouse briefly rhymes, "as they go and come agen so upon the earth do men," which is unusual for a prose version. Rieu aims at readability for a general reader and keeps the narrative moving without obvious stumbles. He cuts the messenger-strand detail in Book 5, giving Athena's speech as a short, pointed push toward Ares, which makes the scene faster. What he removes is some of the texture of Athena's comparison between Diomedes and his father Tydeus. Rouse keeps more of that comparison in and adds the parenthetical "Mr. Facing-all-ways," which translates the Greek "alloposallos" directly but in modern slang. For the Achilles speech in Book 9, both translators give the two fates plainly. Rouse adds "on the road to death" where Rieu writes "on my journey to the grave," and each phrase shifts the tone slightly toward the colloquial or the formal.
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.
An angry man—There is my story: The bitter rancour of Achillês, prince of the house of Peleus, which brought a thousand troubles upon the Achaian host. Many a strong soul it sent down to Hadês, and left the heroes themselves a prey to dogs and carrion birds, while the will of God moved on to fulfilment.
It began first of all with a quarrel between my lord King Agamemnon of Atreus' line and the Prince Achillês.