Greek tragic heroes are defined by the Aristotelian model as set forth in Aristotle's The Poetics. Marlowe's tragic heroes are defined by the Renaissance modifications to the Aristotelian model, modifications which are most famously associated with Shakespeare's great heroes, for example King Lear who embodies both Greek and Renaissance models (he is blinded, exiled, and he dies).
One of the most significant differences between the Greek and Renaissance models, which applies prominently to Marlowe's heroes, is that while in the Greek Aristotelian model, the hero could be punished by either death or something less than death, the Renaissance hero must die. The change came about because of the influence of the different religious system.
In the Greek model, the Greek gods controlled the heroes' fates, therefore blame wasn't wholly invested with the hero. Thus it was seen that tragedy less than death could satisfy catharsis.
The Scene of Suffering is a destructive or painful action, such as death on the stage, bodily agony, wounds and the like. (Aristotle, The Poetics)
In the Renaissance model, the Christian god invests individuals with responsibility for their actions. This supersedes the dominance of gods and Fate. In addition, death was an integral part of Miracle Plays preceding Renaissance theater. These religious factors in combination with the philosophical ideas of humanism influenced the Renaissance hero model so that death was seen as the only right outcome for a tragic heroe's hamartia (flaw).
Thus while Greek heroes like Oedipus, the most oft used example of an Aristotelian Greek hero, could be blinded and exiled, Marlowe's Renaissance heroes had to die.
My God, my god, look not so fierce on me!
Adders and serpents, let me breathe a while!
Ugly hell, gape not! come not, Lucifer!
I'll burn my books!—Ah, Mephistophilis!
[Exeunt DEVILS with FAUSTUS.]
A major difference between Marlowe's tragic heroes and Greek tragic heroes is that the Greek heroes are often brought low by external agencies whereas Marlowe's heroes bring their own doom down upon them by trying to do and achieve too much. Marlowe's heroes are noted for their sin of over-reaching.Tamburlaine would like to conquer the entire world and is too proud and boastful; Faustus makes a deal with the devil in order to gain all knowledge and power. But their excess pride and ambition finally lets them down.
Greek tragic heroes on the other hand are generally condemned by the workings of fate, the wrath of the gods, the fulfillment of curses and so on. For example Oedipus is destined to kill his father and marry his mother even before his birth, and he cannot escape this awful destiny.
Therefore, it might be said that Marlowe's tragic heroes condemn themselves while Greek heroes are condemned by external factors.