Explain the similarities and differences of Homer's Achilles and Virgil's Aeneas.

Both epic heroes share some common features derived from the Homeric texts, but also some substantial differences. 
Aeneas and Achilles are both mighty heroes. They are descirbed with honorific epithets, they are immensely skilled warriors, and they both have divine ancestry. Such a prowess is typical of epic heroes, as it grants them an enhanced status amongst the other characters in the text. They both receive divine aid during the challenges that they are faced with, and both men are, in some regard, influential enough characters that they also receive divine opposition when their deeds arouse the displeasure of any number of the gods. Master-crafted sets of armour are created for both heroes, and both are repeatedly referenced as being subject to the immutable hold of fate.
Although Achilles and Aeneas share some broad qualities, they also have some striking dissimilarities. Where Achilles is motivated by the desire for glory, Aeneas wishes to avoid fighting wherever he can, and acts for the interests of his family and race. Achilles is often self-centred and egotistical, allowing his comrades to suffer in order to further his own ends, whereas Aeneas exposes himself to great dangers in order to protect the future of the Trojan people. Even though Aeneas finds himself subject to bouts of battle-rage that are characteristic of the typical Homeric hero, he prefers to avoid conflict and bloodshed when confronted with adversity, relying on it only as a reluctant last resort.
Aeneas is portrayed with a different characterisation to that of Achilles. The latter is an archetypal Greek hero, exemplifying the heroic qualities of skill at arms and legendary status amongst his fellow soldiers. Aeneas is meant to reflect the ideals of Augustan Rome: contrasting with the inflated ego and borderline hubris of Achilles, Aeneas is described as pious and dutiful, putting the welbeing of his people before any attempts at personal renown. His role as a protecting father and and attentive son underscores his distinction from Achilles, who gave up the chance for a peaceful, domestic life in favour of a brief, bloody, and famous life as a warrior.