Although there are strong parallels between the two works, parallels do not necessarily prove direct influence. There is the possibility that both works incorporated materials from various shared oral traditions or that the epic itself as a genre has certain necessary structural features and themes, such as tales of travel, confrontation with mortality, and attempts to explain the relationship between the divine and human. There has been a great deal of interesting scholarship in the past few decades on the relationship between Greek and Near Eastern cultures, especially by West, Burkert, Morris, and Penglase, but as we do not know the actual identity of the authors of the Homeric epics (or even have any scholarly agreement about the ways in which the epics were authored), and there are no clear and specific references to Babylonian texts in the epic, we must be cautious about ascribing direct influence. 

The first parallel between the two is that both are tales of rulers who suffer, undergoing adventures that are solitary or with small groups of companions, far from the cities they rule. Both are tales of travel to distant and strange places, far from the ordinary world. 

Next, both stories have elements of travel to the underworld, meeting the dead, and discovering the emptiness of life after death. In both stories, we also get a sense that the gods are quite jealous of their powers and routinely punish those mortals who become too powerful or attempt to challenge or equal the gods. The protagonists of both stories have some elements of divine ancestry, and gods routinely interfere in their lives.

Finally, both stories have strong contrasts between good and bad rulership. Gilgamesh starts as a bad ruler and becomes a good one. Odysseus is a good ruler contrasted with the suitors, who are emblems of the misuse of power. Thus both stories end up as "mirrors for princes," or stories that can serve as guidance for the aristocrats listening to them on how to use power wisely and well.

In both the Epic of Gilgamesh and Homer's Odyssey, mortals combat some gods and are aided by other gods. Gilgamesh who, like Odysseus, travels a long way from home, tries with his friend Enkidu to enter the forest forbidden to mortals. To do so, he must fight a monster who belongs to Enlil, god of the earth, and he is aided by the sun god, Shamash. Similarly, Odysseus must do battle with the Cyclops, the son of Poseidon, god of the seas, and he is aided by Athena, the goddess of wisdom, in all his travels. Gilgamesh, like Odysseus, must fend off goddesses. Gilgamesh refuses the attentions of Ishtar, the goddess of love and war, and Odysseus decides not to stay with the semi-immortal nymph Calypso in favor of returning to his wife, Penelope.

Like Gilgamesh, who learns about friendship but loses his friend Enkidu, Odysseus befriends the men who are returning from the Trojan War with him. Odysseus also loses the men on his ship and suffers greatly. After returning to Uruk, Gilgamesh becomes an upstanding leader, dedicated to improving the lives of the people he rules. Similarly, Odysseus, after his travails and his return home, becomes again a respected leader of Ithaca and a devoted father and husband. Both men are mortal but are heroes among men.