In the Iliad, Achilles is faced with two choices which he learned of through his mother, Thetis, which are kleos,”fame,” and nostos, “homecoming.” If Achilles decides to return home, he will lose his kleos, but will have more time at home and an unchallenging death. Though if he stays in Troy and fights his nostos will be lost, but he will obtain kleos. Achilles understands that living would be an extension of time, but that just time itself has no value. At first he chose nostos and after the shift in his anger towards Agamemnon he chose kleos.
I think that kleos is more important to pursue, because overall to the Greeks kleos means that you and your story will live on forever and that was very important to them. Even though Achilles was