Oedipus and Hamlet are two very well known characters in literature. They both stand out in a reader's mind through their actions, conflicts, strengths, and weaknesses. A reader becomes involved more in the action through these two characters. They allow us, the reader, to gain a greater sense of the stories plot. In many ways these characters hold similar traits to one another but the one that stands out most in my mind is their relationships with their fathers. Their father's prior conflicts and decisions influenced these characters to the point of their own demise.
It is hard to compare two men with such obvious religious and moralistic differences. Oedipus grew up in the time of the Greek gods, gods who set their examples through destruction of the titans, incestuous marriages with siblings, and rash actions that changed the way their followers lived. Hamlet, on the other hand, grew up with strict Catholicism shaping his conscience. He followed that conscience to the letter, allowing for the lengthy period in between the revelation of the ghost to the actual bloodbath in the closing scenes.
This lapse is what sets the differences between Oedipus and Hamlet, for as soon as Oedipus had the truth fully revealed to him, he acted, rash as his actions may have been. By far, Oedipus is the more thorough of investigators, but this is due mainly to his hubris that will not allow otherwise.* Hamlet took his time to trap Claudius into admission of guilt, whereas all of Thebes knew that Oedipus was on the lookout for a murderer.
Both protagonists were passionately determined to find the truth.
Both were impulsive.
Both had immense self-pride, but--
Ultimately, both were good natured.
They seek revenge for their fathers (although this is ironic in Oedipus Rex)
Although O's arrogance may have led to his downfall, it is their impulsiveness that does in each man: O's decree of exile parallels the gods' requirements, but Hamlet's stabbing of Ophelia's father right after NOT stabbing Claudius means that, in the grand scheme of things, he will have to die rather than assume the throne.
Both plays are tragedies that result from behind-the-scenes machinations--the gods plot against O's family because of Laius, while King Hamlet's brother plots against him.
Perhaps the vivid imagery of poison in Hamlet parallels the curse "in the family blood" in Greek tragedies ...