I think that the fundamental similarity between both Arthur and Odysseus is the craving for order and unity in the world. Both heroes are animated by the idea of establishing or reestablishing order and function to a world that might lack it. Arthur is convinced of the sincerity of such a goal, and this ends up driving his quest in his legend. His establishment of the Round Table is evidence of this. His need to only wage a just or necessary war is another example of this. Finally, Arthur's desire to obtain the Holy Grail as a need to unify the realms of mortality and immortality as well as the fundamental belief in justice and honor are all examples of how Arthur craves order in the world and shows this in his quests. Odysseus is much the same. His need to return home is representative of a desire to bring forth unity and symmetry in his own state of being. This is something that Homer also sees in his protagonist, evidenced in the fact that the Assembly in Ithaca has not met since Odysseus' departure. In this, there is a belief that Odysseus' return implies a form of civic order. The suitors who have come to occupy his home represent an element of disorder, something that order, in the form of Odysseus, will restore. In general, the disorder in the Trojan War will be set back and calibrated to order with Odysseus' return. In both heroes, the craving for order, unity, and symmetry becomes a primary motivation for both heroes in their respective quests.