His failure at both appears to perpetuate each other: his failure as provider translates to his failure as business and family man, and indeed to his failure as American success. In this way, the American Dream is representative of ultimate success. By failing at this, Willy represents the doubts and fears of many Americans; he fails in all the ways feared by society.
Oedipus' failure occurs on a much larger scale. His success relates to his status as the person of highest importance in society. He however reacts differently from Willy, who first lies to himself and then crumbles under the pressure of the increasingly obvious truth. As the truth becomes increasingly obvious for Oedipus, he still refuses to turn away from his search. When all is finally revealed, Oedipus displays his true character by taking responsibility for his actions. Although the king can hardly be blamed for what happened, he nonetheless believes that he has committed a terrible crime and devises a punishment that he believes he deserves; he blinds himself.
Willy in contrast refuses to take any responsibility for his past behavior or present situation. Instead, another of his subtle mistakes is blaming others instead of himself for his failure as a business and family man. He blames his boss for his failure in the former and his sons for not being what he wanted them to be. None of this is detected in Oedipus, who refuses to blame even those bearing most guilt for his situation. He blames only himself and remains alive for his punishment. Willy chooses the coward's way of suicide, and in the end cannot enjoy the final reprieve from his financial difficulties.
The main difference between Oedipus and Lowman is the distance of their fall. Willy's cowardly fall at the end is not a great leap from the beginning, where he was basically a failure at everything. Being unable to break his downward spiral, Willy commits suicide. On the other hand, one could also see Willy's action as a final act of nobility at the end of a very humiliating life. Perhaps in the society that formed him, suicide was the only final attempt at nobility that was an option for Willy. In this, he is parallel with Oedipus, also a product of his society. Oedipus believes it would be best not only for himself, but also for his people if he were to step down as king and made a public display of his humiliation and pain. Oedipus however fell much farther than Willy in concrete terms from the beginning to the end of the play. He begins as the ultimate symbol of success for the society of his time. At the end, he is humiliated and all sources of power are removed from him. Willy on the other hand is humiliated throughout the play. It simply became overwhelming for him, and therefore not even his death has a shred of nobility to it.
In considering Aristotle's definition then, Oedipus' character is much more parallel to the concept than Willy. Oedipus is noble, filled with pride in himself and his own accomplishments. He comes to a fall, but reacts by taking responsibility for his circumstances and his actions. Willy on the other hand was already fallen when the play began, and was therefore not required to fall much further. Both characters lose everything after the final scene of punishment: friends and family members are left behind or killed through the actions of the tragic heroes. Willy however gains to wisdom, whereas Oedipus accepts that his death will accomplish nothing.
When considering the two heroes, it is important, as mentioned above, to understand that each acts as a tragic hero for his society. Will Lowman appeals to the society of modern America, where ambition and success or the most important achievements. Oedipus' society on the other hand hold the king in high regard. Hence I would argue that both men play a tragic role in their respective plays. It is therefore necessary to also understand that literature emerges from society and therefore presents the reader with a mirror of the values on that society.
Miller, Arthur. Death of a Salesman Penguin, 1976
Johnston Ian. Fate, Freedom, and the Tragic Experience: An Introductory Letter on Sophocles's Oedipus the King. 2007. http://www.mala.bc.ca/~johnstoi/introser/oedipus.htm