Both of these characters are of course famed for their heroic exploits and bravery, and both of these texts present Wart and Odysseus respectively and living up to their reputation. However, the chief difference is the way that Wart is presented in White's novel not as a fully-fledged epic hero in the same way that Odysseus is presented. What is so fascinating about The Once and Future King is the way that the character of Wart is all-too human in his various failings. Whereas Odysseus is shown to be brave, courageous, intelligent, cunning and resourceful, The Once and Future King presents a picture of the future King Arthur that shows his human side.
Odysseus shows that he starts the action in The Odyssey as a fully-fledged hero who is well equipped and resourced to encounter and triumph over all the various trials and tribulations that he faces. He has great strength, bravery and cunning, and he employs these traits to great effect to ensure his safe arrival back at Ithaca and his return to his beloved Penelope and his son Telemachus. Wart, by contrast, is shown to be just an average honest individual who is not too bright. The focus on the lessons that Merlyn tries to teach him shows that he has to work very hard to grasp the point of Merlyn's teachings, and even after this process of education occurs, Arthur is still shown to struggle as King in his attempts to preserve peace and rule with justice.
Therefore I would argue that the key difference between the presentation of these two characters lies in the way in which Odysseus is presented as the stereotypical epic hero who is already fully-formed and who engages in various heroic deeds. The emphasis in The Once and Future King, on the other hand, is to stress Wart's humanity and his failings, focusing on the way that he is not your average epic hero.