Achilles was the hero of Homer's Iliad. The entire epic is focused on the "wrath of Achilles", or the period when Achilles withdrew from the fighting because he was angry that Agamemnon took his war prize. What made Achilles a hero was his prowess as a fighter. He is portrayed as brave and powerful, with a strong, if somewhat narrow and selfish, sense of honour. His abilities as a fighter made him able to turn the course of a battle by sheer physical skill and strength.
Aeneas, the protagonist of Virgil's Aeneid, is a more complex and modern character. As a prince of Troy he is responsible for leading his defeated people to safety. He is constantly torn between his duties as a leader, the commands of the gods, and his own desires. While Achilles is a flat character, typical of oral traditional epic, Aeneas is a more rounded character, with a rich internal life, who develops over the course of the poem.