First of all, characters in both books make mistakes. Examples of this are when
Odysseus reveals his true identity to the cyclops, Polyphemus, and when Rorschach walks right into a trap. Both mistakes could have been prevented by the character.
Odysseus was safe from danger when Polyphemus knew him as Nobody, but he made the blunder to reveal himself just before he left. Rorschach should have been more suspicious about a note to go to Jacobiʼs apartment. He walked right into the copsʼ hands. The difference is that many of Odysseusʼs mistakes were a result of his pride, while Rorschachʼs were more results of him not being careful.
Secondly, characters in both books display complex emotions. The characters have realistic reactions to events. An example of this in Watchmen is the scene on
Mars. In the beginning, Laurie was getting aggravated at Jon for various reasons. When she discovered that the Comedian was actually her father, she gets very upset and breaks down. And example in The Odyssey is when Odysseus becomes very homesick.
He sits outside and cries until Calypso says he could leave. The characters in The
Odyssey have more subtle emotions, while Watchmen is written so you can hear the emotion clear in their voice.
Third, the characters change throughout the books. Dr. Manhattan definitely changes through the book. He starts off distant to other people because he sees them as nothing special. Then he had a revelation and regained his appreciation for human life. Odysseus changes as well. He starts off proud and a little brash. Through the book he learns how to be more patient and how to swallow his pride. Prime example of this is when he was disguised before he confronted the suitors. He got mistreated, but he held his tongue. The difference is that Odysseus slowly changed, while Dr. Manhattan changed very suddenly.
Overall, Watchmen and The Odyssey are very different books. However, they have similarities in characterization. The characters of both books make mistakes, show realistic emotion, and are changed by the events of their journeys. They are shown differently and are used differently, but they exist in both to make the characters more realistic.