The difference in cultural values between Homer's Greece and Virgil's Rome can be evaluated through a study of Achilles and Aeneas. Both are sons of goddesses, both are involved in the great Trojan War—though somewhat tangentially motivated by its initial cause—and both are ultimately defined by this war.
Achilles has a choice regarding whether to participate, and he goes into battle knowing that he is trading long life for glory, which is not an insignificant value in ancient Greek culture. If the Greeks' great dictum is to "know thyself" and if happiness is based on the concept of human flourishing (a quality of personal development through individual virtue or integrity), Achilles's desire for glory should not be seen as selfish or arrogant. His epithet is "like to the gods," but his true greatness eventually shows itself in his superior humanity. He seeks to be the best participant in the type of action on which the ancient Greek might prove himself, and ultimately he demonstrates his superiority in battle, in friendship, and—perhaps most importantly—in acknowledging the human dignity of his enemy, Priam. The late episode in which Achilles meets with Priam and returns Hector's body to him shows the measure of Achilles's humanity, which ultimately overtakes his measure as a great warrior.
Aeneas, by contrast, begins his epic journey by assuming the burden of carrying the legacy of Troy to a new nation, Rome. His epithet is "pious Aeneas," and the classic image of him shows him carrying his father on his back, guiding his son by the hand, and carrying the household gods. This idea of being faithful to one's father, to one's own role as a father, and to one's fatherland defines Aeneas's virtue. He abandons much of his individuality, his personal desire to join with Dido, and his human passions to serve his mission to found Rome. The Roman values of duty to country or ruler, perseverance, and self-denial mark Aeneas's growth in the epic. Virgil seeks to draw parallels between his epic and Homer's, but in most instances, we see that Virgil is fully on the side of the larger Roman enterprise than he is on the side of the individual as Homer is.