Macbeth's tragic flaw is usually considered to be ambition, rather than greed. And Shakespeare is Shakespeare because he transcends those writers that came before him. He takes the classical and reinterprets it and goes beyond it.
Macbeth, instead of the traditional realization of his wrongs, realizes how meaningless existence is: it is a tale told by an idiot, signifying nothing. He understands how meaningless his conspiracy and tyranny have been.
Just because Macbeth may not fit exactly the classic definition of a tragic figure, doesn't mean he is not one. I would argue, in fact, that the lack of redemption is an improvement, and certainly a step toward the modern and postmodern.
Often readers suggest that Macbeth is a tragic hero because he possesses tragic flaws, namely greed. However, in Aristotle’s definition of the tragic hero, the punishment that the hero receives outweighs his actual crime and the hero must arrive at a stage of knowledge and redemption at the end of his journey. Macbeth commits murder during his reign, so one could argue that his own death is fitting punishment for having taken the lives of Duncan and Banquo. Further, Macbeth never truly realizes his wrongs; he simply realizes that the army in the forest outnumbers him and the few supporters that he has left. So for these reasons, Macbeth really does not fit the classic definition of a tragic hero.
Macbeth is both. First, he is a tyrant because he rules without restriction. In other words, he is not held to make decisions within a government that checks and balances power. Macbeth can make any decision he'd like without consulting another person or having an idea approved.
Moreover, "tyrant" denotes ruling harshly. In order to stay in power, he kills anyone who threatens him or who he perceives to threaten him. Macbeth has no moral center and thus cares little for the well-being of others. Because the play reflected Elizabethan-era themes, when Macbeth threw off the balance of power by killing King Duncan, the entire society was in chaos. However, Macbeth cared little for his political responsibilities of caring for his citizens and more on safeguarding his position as king.
If you had to pick between "tyrant" and "tagic hero", the play focused more on Macbeth as a tragic hero. A tragic hero, by definition, is someone whose downfall is marked by an error or significant flaw. Macbeth's flaw, unchecked ambition, was at the center of his downfall. His hunger for power led him to kill those whom he loved most. Because he had a moral center in the beginning of the play, the murders haunt him and his paranoia leads other to be suspicious of him. The suspicion turns into a mass revolt that takes Macbeth's life.
Macbeth is in some respects both. He is presented as an usurper of the Scottish throne, having assasinated his king, Duncan. His own rule is as bedeviled by revolt as his victim's was, and Macbeth and his wife are summed up by Malcolm as "this dead butcher and his fiendlike queen." On the other hand, he does express remorse for his murder, and he and his wife suffer the lack of children as a result of their actions. He exhibits hubris, like all classic tragic heroes, and an unsettling knowledge that man's fate in this world is mystifying and tragic. As the Pelican edition of Shakespeare's works states, the witches introduce "something the play both overtly denies and implicitely articulates: that there is no basis whatever for the values asserted on Duncan's behalf; that the primary characteristic of his rule, perhaps of any rule in the world of the play, is not order but rebellion."
Of course, Macduff is the actual hero of the play, but of all Shakespeare's plays this is the most morally ambiguous. Malcolm has vices which Macduff condones, Macduff himself essentially abandons his family. Unlike the other tragedies, in which good obviously triumphs over evil, this play is somewhat ambivalent, in the end.
As an interesting aside and possible partial explanation of the dual tyrant/tragic hero nature of Macbeth and ambiguousness of Macduff as a hero, the actual history behind the play is quite different from Shakespeare's version. In reality, Lady Macbeth had children from a previous marriage, who were the legitimate heirs to the Scottish throne, which Duncan had seized from Macbeth's wife. The "murder" of Duncan was a political assasination which made the real-life Macbeth a national hero, and his conquerors were essentially traitors who delivered the Scottish nation to England.
Are you serious?
macbeth is both tyrant and tragic hero. in the begining of the play, maacbeth is a tragic hero because he defends his country by fighting in the war in scotland, however when he returns and the witches tell him that if he wants to be king, he must kill Duncan, which will return the favour of him being king. however, King Duncan, is Macbeths friend, so At first Macbeth thinks its wrong and he doesnt want to do it. but then Lady Macbeth says "it is too full o'th'milk of human kindness" which means " your not man enough" So Macbeth decides to kil duncan.