The fact that he believes in the gods differently than some of his neighbors seems to cause them to view his teachings as atheism. In the "Apology," Socrates says: "Some one will say: And are you not ashamed, Socrates, of a course of life which is likely to bring you to an untimely end? To him I may fairly answer: There you are mistaken: a man who is good for anything ought not to calculate the chance of living or dying; he ought only to consider whether in doing anything he is doing right or wrong, acting the part of a good man or of a bad." This sense of pursuing goodness does not mean that Socrates believes he will necessarily have a better place in the afterlife. However, Socrates believes that to act morally is its own reward, not something that will win him favor in the eyes of the gods, or even human esteem. In "Gilgamesh," the epic life of the hero is often characterized by violence and blatantly unethical actions, such as the violence Gilgamesh frequently inflicts upon others during his rule. The hero, until the death of his friend, seems uninterested in anything with implications about the life beyond. Confronted with the grim reality of death and the afterlife, however, rather than resolving to make his brief life on earth as fruitful as possible like Socrates, through moral deeds, Gilgamesh instead resolves to find the secret of eternal life and becomes a philosopher of sorts as a result of his life's circumstances.

But both men confront the tragedies inherent to human existence. Gilgamesh's friend Enkidu is rather arbitrarily singled out for the vengeance of the gods, just as...

Even those who live eternally in "Gilgamesh" do so by accident, not by design or cleverness. Socrates lives in a world where no one has eternal life, therefore his capriciousness about whether he lives or dies -- for Socrates, the reward and satisfaction comes from knowing life has been lived well, as that is all one can hope for. And even Gilgamesh, for all of the narrative theatrics he suffers over the course of his tale, learns that a certain sense mindset must be achieved in life, to make life bearable. In "Gilgamesh" the only peace comes with acceptance of the morally neutral nature of human life. Socrates might not agree with "Gilgamesh" and its advocacy of passive acceptance of the fact that there are no answers to the meaning of life and the cruelty of the gods, as Socrates actively struggled with the need to find satisfactory answers to moral questions. But he would agree that the will of fate, or of the gods, or whatever he called the divine forces affecting human life, could not be reasoned with, that one could only search for truth, even in the equally arbitrary and capricious face of political misunderstanding. Both Gilgamesh and Socrates believed humans could only use reasoned actions and thoughts within themselves to deal with those arbitrary forces.
Works Cited

Plato. "Apology." From the Dialogues of Plato: Volume 2. Translated by Benjamin

Jowett. Oxford: Oxford University Press, 1892. 19 Nov 2007. http://www.law.umkc.edu/faculty/projects/ftrials/socrates/apology.html