The following excerpt from "The Tragic Hero: From Oedipus to Batman" implies that the character Macbeth is similar to the character Oedipus in Oedipus the King by Sophocles: Earlier in the story, he gets in a fight with a man riding a chariot, which ends in the man's death. Oedipus doesn't know it, but the stranger he kills is King Laius of Thebes. What Oedipus also doesn't know is that King Laius is his father. You see, Oedipus was abandoned as a baby and grew up in a different city, never knowing his parents. In fact, once he makes it to Thebes, the people are so thankful the Sphinx is gone that they decide to make him king, so he marries Queen Jocasta, who just happens to be his mother. In your response, argue that Macbeth's tragic hero status is actually different from Oedipus's.

As the other answers indicate, Oedipus killed his father unknowingly, while Macbeth knew exactly what he was doing in his premeditated murder of Duncan. Oedipus was, in fact, trying to flee the prophecy when he left Corinth and met his father on the road to Thebes. Macbeth almost backs out of his murderous plan, but at his wife's urging plunges forward.
However, what these different beginnings lead to is the key difference in the two men's tragic trajectories: Oedipus moves from pride and blindness to humility and virtue. Macbeth moves in the opposite direction, from decency, courage, and conscience to become a hardened tyrant filled with bitterness and despair. Oedipus, through tragedy, moves from vice to virtue. Macbeth, in contrast, moves from virtue to vice. Macbeth creates tragedy through a consciously evil act and multiplies it until he is dehumanized and without insight. Oedipus blinds himself but gains humanity and insight.
Oedipus as tragic hero teaches us we should cultivate humility because we can't control our fates. Macbeth as tragic hero teaches us that violating moral law to satisfy our ambitions—i.e., knowingly doing evil—destroys both us and the people around us.

Macbeth's status is a tragic hero is very different from that of Oedipus. For a start, Oedipus did not plan to kill his father. It happened as a result of a fight between the two men. In contrast, Macbeth plotted to kill King Duncan because he wanted to take his throne. Macbeth's desire for power far outweighed any respect and love that he felt toward Duncan.
In addition, while Oedipus is made king by the people, Macbeth takes the throne before the true heir, Malcolm, has the chance to do so. In fact, as soon as Duncan is dead, Macbeth travels to Scone to be invested, leaving the reader in no doubt of his ambition.
Finally, we can see further differences between these two men when we look at their wives. Lady Macbeth, for example, contributes to Macbeth's downfall because she drives his ambition and chastises him when he loses the courage to kill Duncan. Without her, there is a chance that Macbeth might never have killed Duncan. In contrast, we see no such malice or cunning in Queen Jocasta. Her only crime is marrying her own son. However, she did not know his true identity at the time of their marriage.

When Oedipus murders King Laius, his biological father, he does so unknowingly.  Further, Laius had actually been aggressive toward Oedipus when they ran into each other on the road.  Oedipus only thought that he was killing some stranger, a nobody, who had treated him violently first (remember, too, that Oedipus grew up as the prince of Corinth, so he's used to respectful treatment, and Laius, as the king of Thebes, was used to being treated deferentially as well -- so, lots of pride in that interaction). 
On the other hand, when Macbeth kills King Duncan, he does so with his eyes wide open, in full knowledge of who he's killing and why.  He kills his kinsman, his king, his guest, and his friend, all in one, and he does so in order to usurp the king's power and position.  Oedipus does not; he's not trying to achieve power, he's just trying to get some answers.  This is just one reason that Oedipus seems to be a much more sympathetic tragic hero: he only wants the truth -- a truth which has been withheld from him for his whole life.  Macbeth doesn't pursue truth; he pursues power, and this makes him a lot less sympathetic of a tragic hero.