Achilles and Gilgamesh have many similarities and differences as epic heroes; for example, their obsession with death and immortality and their reactions to the deaths of others. Both Achilles and Gilgamesh lose close friends, but the difference is how this loss affects them.
According to the Center for Hellenic Studies at Harvard University, both Achilles and Gilgamesh struggle with their mortality and reach a certain degree of acceptance or understanding in this struggle. Both Achilles and Gilgamesh are half divine and half mortal. Achilles is the son of goddess Thetis and mortal Peleus while Gilgamesh is the son of goddess Ninsun and mortal Lugalbanda. Both seek to find glory and immortality in battle. Both are imminent warriors. Both must also face the loss of close friends.
The contrast is in how they deal with this loss. Both Achilles and Gilgamesh become somewhat wild and uncivilized, killing others and refusing to die; however, at a certain point Achilles accepts his fate, knowing that death is inevitable. Gilgamesh, on the other hand, fears death and seeks everlasting life, which he fails to find. Also, Achilles believes that dying with glory in battle is not worth death, while Gilgamesh fears death because it will stop him from finding glory in battle.