Throughout the epic Odysseus is portrayed as a very confident man. Not only is he confident in his abilities as a leader and warrior, he also is confident in his overall person. He is a very good looking man. However, when Homer describes Odyseus in the most striking light, he is always being "lavished" his god-like looks by Athena. She is the reason he looks as intriguing as he does when Homer takes the time to cover all of his features. In Book XXIII, Homer has Athena work her magic on him once again for Penelope.
She "made him look taller and stronger than before; she also made the hair grow thick on the top of his head, and flow down in curls like hyacinth blossoms; she glorified him about the head and shoulders just as a skilful workman who has studied art."
As he steps out in front of Penelope, he looks like an immortal. These are the only times that he is described in such detail. Therefore, his appearance never has much bearing on who Odysseus is. He is known for his wit and his abilities at war. If he was conceited about any other aspect of himself, it would be the former two traits.
I have to agree with troutmiller here. Throughout the epic poem, we see Odysseus praised by others for his strength, his cunning, his intelligence, his heart, and his bravery. We can infer that he's not a poor specimen of male beauty the way the other immortal women (Calypso and Circe) fawn over him, but Homer doesn't focus on his physical over his charismatic traits.
This is a vast difference from the main character who is supposed to parallel Odysseus in Oh Brother. He does have a great deal in common with him in the sense that he is highly devoted to his friends while still being too proud and self-involved to realize he is risking their lives in attempt to save his own. There are many parallels you could draw. Keep looking!