Both translations are prose, but they land in different registers. Butler writes in a measured, Victorian cadence that stays formal throughout. His sentences run long and even, with a slightly elevated diction: "many a brave soul did it send hurrying down to Hades." Rouse writes shorter, quicker sentences and uses a plainly modern voice. In the Book 5 passage, when Athena calls Ares a troublemaker, Butler gives "villain incarnate, first on one side and then on the other," while Rouse writes "Mr. Facing-all-ways." That phrase is colloquial to the point of being breezy. In Book 6, Rouse turns the famous leaves simile into something close to a rhyme: "as they go and come agen so upon the earth do men," which Butler handles without any rhyme at all. Butler follows the Greek sentence structure closely and keeps the epithets and repetitions that Homer uses as structural markers. This gives his text a consistency that reflects the oral-formulaic nature of the original. Rouse removes many of those formulas and rewrites for immediate readability. In the Book 9 passage, Butler cuts Achilles' speech to its emotional core: "If I stay here and fight, I shall not return alive but my name will live for ever." Rouse gives the full conditional structure of the Greek, both branches of the choice in equal length. Butler's cut gains force; Rouse's expansion keeps the logical shape Achilles actually uses. In Book 21, Rouse adds "morning or evening or midday," which is in the Greek. Butler omits it entirely.
Sing, O goddess, the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down to Hades, and many a hero did it yield a prey to dogs and vultures, for so were the counsels of Jove fulfilled from the day on which the son of Atreus, king of men, and great Achilles, first fell out with one another.
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.