Both men act both heroically and unheriocally throughout The Iliad. However, given the ancient Greek assessment of heroism - pursuit of kleos, skill in battle, and dedication to the family, amongst others - Hektor must be considered the better hero.
Hektor, though he runs away from Achilles, inciting the chase in Book 22, stands up to Achilles and faces his fate. He says that Achilles will have to stab him in the chest, as he will not see his back. Hektor is dedicated to his family, though it could be said that he abandons them in pursuit of kleos, leaving Andromache to the threat of enslavemnet and Astynax to die. This desire for glory, however, embodies him a good ancient hero.
Achilles lacks control, abandoning his men as a result of his anger at Agamemnon. He is an exceptional warrior, a key trait for a good hero, but does not utilise this skill until after Patroklos is killed. Therefore, his selfishness, particularly when set against Hektor's selflessness, makes Hektor the better hero to me.
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