Again, I'm a bit late in responding to your request as you already have answers, but I'll make my contribution just the same.
In The Poetics, Aristotle defines tragedy as an "imitation of an action" that is serious and not trivial and that has "magnitude," or great importance, and that is "complete in itself," we might say having beginning, middle and justifiable end. He further says the events should arouse "pity" for the hero's circumstance and "fear" for the hero as consequences approach. Aristotle states that pity and fear provide the "catharsis" of the emotions within the play--fulfill it's emotional resolution. In more general terms, tragedy is defined as a literary drama in which the hero suffers a horrible fate.
Aristotelian tragedy emphasizes several other points as requirements to tragedy. Some are: (1) Events should be complete, representing a total reversal of the hero's fortunes. (2) The hero must be a person of renown with superior attainments. (3) The language should be that of poetry with elevated diction and "embellished with every kind of artistic expression," meaning taking advantage of many literary techniques. (4) The drama must provide a catharsis of its own action so that the ending resonates with the magnitude of the drama, thereby providing a "catharsis" (washing away) of the pity and fear aroused by actions within the drama. (5) The hero cannot be purely good or purely evil, but must be a superior person who has human qualities and fallibility. (6) The tragic end of the hero results from a mistaken action that itself arises from an error in judgment (tragic error) or a personal flaw in character (tragic flaw). (7) The hero need not die; other tragic consequences may serve the catharsis of the tragedy (e.g., blinding, exile).
Elizabethan/Shakespearean tragedy takes several divergences from Aristotelian tragedy. Some of which are: (1) Shakespeare abandoned the Aristotelian unities of action, time, and place (e.g., Hamlet covers many months) although Ben Jonson insisted on maintaining the unities. (2) Shakespeare innovated tragedy by creating romantic tragedies with grand sensation, such as Macbeth. (3) Greek tragedy used the Chorus to report battles and other horrific events, whereas Elizabethan/Shakespearean tragedy began to show these onstage. (4) Shakespeare deviated from Aristotelian requirements by adding passages of prose in with the poetry. (5) Elizabethan/Shakespearean tragedy required death as the appropriate outcome. (6) Tragic character flaws overtook tragic errors becoming sole causes of the tragedies. (7) The Aristotelian Chorus is replaced by Fools and Clowns who continue the Chorus function of delivering plot points and plot information; they are particularly useful in revealing information about characters. (8) Catharsis came to mean a purging of vile tendencies from the audience by a cathartic identification with the character flaw and tragedy of the hero: catharsis shifted from a focus within the setting to a focus on the audience.
Some key differences between Aristotlian tragedy and Shakespearean tragedy are as follows:
- the elimination of the chorus in the Elizabethan tragedies,
- the "tragic flaw" differs from Aristotle's hamartia, or tragic mistake. For example, Antigone's desire to see her brother decently buried cannot be construed as a tragic flaw.
- the presence of more supernatural elements in Elizabethan tragedies
- the consistently tragic ending for Elizabethan tragedies. Classic tragedies did not need to end in tragedy whereas Elizabethan tragedies end with death. For instance, in Oedipus at Colonus, the hero finds a peaceful death after years of suffering in order to atone for his misdeeds.
- The tragic hero of Shakespeare does not always gain in self-knowledge before his death as does the hero of Aristotle's tragedies. For instance, Macbeth pursues his path of rampant murder to the end.
I can give you a few details to help you on your way to an answer or "discussion," as you refer to it. My answer will assume you know the basic characteristics of tragedy, such as tragic figure, tragic flaw, catharsis, etc. All of these are contained in Elizabethan tragedy and were originated by and taken from the Greeks.
Elizabethan tragedy did build on what it inherited, though. I say "build on," but some might see this as a negative development, as a corruption, possibly, of Greek thought concerning tragedy. In other words, if you view Greek tragedy as the highest level of tragedy, than variations from it might be seen as corruption.
Positively or negatively, though, Elizabethan tragedy does vary from Greek tragedy.
One place for you to start would be with a contrast between Shakespeare's Macbeth and his Hamlet.
Macbeth is very much classical. Fate plays a large part in the play, although it takes a slightly different form: predestination/determinism and free will are the issues here. And the form of the play is tight and streamlined. The tragic flaw is evident and consistent, as is the need for cleansing. From early in the play, Macbeth's treachery and tyranny is clearly evident, and the need for him to be destroyed is definite. Ambiguities in motivation are not present.
In contrast, Hamlet, is "all over the place," one could say. Fate does not play a role in the play, and Hamlet's tragic flaw is ambiguous (we know he delays in taking revenge, but numerous possibilities exist that might explain why). For at least part of the play, the guilt of the antagonist, Claudius, is doubted. And classical-like balance is not maintained. The play, in a sense, rambles: Hamlet has a chance to kill Claudius and doesn't, he is sent to England, he partly walks back to Elsinore and happens across a grave being dug, he seems to take forever to enact his revenge. He also gets side-tracked and wastes much time worrying about his mother's role as wife to Claudius.
Many consider Hamlet more romantic than classic.
These two plays represent Elizabethan drama imitating classical drama, and varying from it.