This sounds like an essay topic, so I'll give you a few points of comparison to get you started. Please also use the link below to more information on writing a comparison/contrast essay.
- Probably the most important difference between the two is that Brecht wanted his audience to think intellectually about the performance that they were witnessing, while Aristotle argued that audiences, especially those witnessing a Tragedy, should be drawn in emotionally, experiencing the tragic circumstances along with the hero of the play.
- Aristotle did not actually write or produce theatrical performances, he was a philosopher and offered theoretical ideas about the nature and purpose of drama in his work Poetics. Brecht was a director, writer and producer of his own theatrical productions. So, while Aristotle presented theoretical ideas about theatre, Brecht presented practical applications or stagings of actual performances.
- Aristotle proposed that the drama (especially Tragedy) is a journey of a main character to a cathartic self-awareness. For Brecht, dramatic theatre exists as a vehicle to create social change, not to reflect the internal workings of an individual soul. So, Aristotle's focus was man's internal life, while Brecht's focus was on the external, the social order.
For more on Aristotle, his Poetics, and Brecht, plus some tips for creating a comparison/contrast essay, please follow the links below.