The Odyssey and Iliad are very frequently pointed to as supreme works in epic form. How do they seem to vary from Gilgamesh in terms of epic qualities? How do they reiterate the epic qualities of Gilgamesh?
First, while the Homeric epics were among the earliest and best known of Graeco-Roman epics, and were considered models of the Greek epic form, the western tradition of Graeco-Roman antiquity is not the only epic tradition. The Indian Mahabharata and African Sundiata, the Coyote tales of the Navajo, and the Japanese Tale of Heike are all representative of their own important traditions, and in those cultures the Homeric epics would not be considered "supreme".
Gilgamesh was written nearly 2,000 years before the composition of the Homeric epics, and represents a quite different cultural tradition. Unlike the Homeric epics, the form in which we have Gilgamesh is a literary form rather than a transcription of improvised oral performance. This means that Gilgamesh lacks certain of the features of oral epos such as a high degree of redundancy and use of epic formulae that we find in Homer. Also, because Gilgamesh is a foundation story about a single king, its plot structure involves far fewer characters than the Homeric epic.
Although the heroes of Homeric epic are descended from gods, they themselves are mortals, impressive and powerful, but nonetheless limited; Odysseus may be stronger than the suitors, but he is not a god. Enkidu and Gilgamesh are more godlike than the Homeric heroes, often displaying superhuman strength and endurance. This reflected the difference between the aristocratic society of archaic Greece and the centralized palace-temple complex with a single king who acted as conduit between gods and people found in Sumer.
The Homeric epics are similar to Gilgamesh in transmitting culturally important information, involving both gods and humans, serving as foundation stories for their cultures, and involving heroic conflicts.