What are the differences between epic theatre (Brecht), and realistic theatre (Ibsen)? How can we compare them based on their plots (linear plot and episodic plot), emotion and thinking, and stage design?
The previous educator very succinctly and aptly described the differences between epic theatre, as interpreted by Bertolt Brecht, and realistic theatre, as interpreted by Ibsen.
I would add that both expect strong emotional reactions from the audience, but they pursue those reactions differently. As previously mentioned, Ibsen and the realists wished to mimic reality on stage; Brecht, on the other hand, believed that art shaped reality—not the other way around. This is most strongly evident in his dialogue.
Ibsen, in his effort to recreate "natural" situations, wanted language to sound natural and worked to ensure that each character in his play had a distinctive voice. In his pursuit of a "natural" sound, he constantly revised his plays until the lines sounded completely credible. He relied very much on the reactions of the audience in determining whether or not he had succeeded in providing the illusion of reality on stage.
In contrast, Brecht's characters often sound nonsensical. Moreover, he was not interested in individual characters but instead in the social structure they represented. He loathed the conventions of realistic theatre, as developed by Ibsen, due to his perception that they created passivity in the audience. Instead of dialogue, he would sometimes use parables, which might have taken the form of song. This convention is displayed in Mother Courage and Her Sons. Again, like Ibsen, he wished to draw attention to political concerns (e.g., the rise of Nazism), but he would not allow the audience to lose themselves in a story that was reflective of that concern, as one could do when watching A Doll's House, for example. He was not afraid to alienate his audience by fracturing scenes and ignoring Aristotle's ideas about theatre, as written in Poetics.
Arguably, Brecht's style was better suited to the Modern era, which had already established non-linearity and nonsensical language as conventions in literature (e.g., Ulysses). Because Modern art and letters challenged both the nature of reality as well as established conventions in art, theater-going audiences were more receptive to Brecht's urges to break the rules of theatre.
Epic theater calls attention to its own staging and in many ways disrupts the illusion that is created in the theater. The plot may tend to be more episodic, with clear ruptures and visible (not hidden) scene changes. The stage design may be minimal and may include space, for example, for people to walk around with signs that challenge or even insult the audience. I remember reading in my German literature classes about signs that Brecht would use saying things such as "Don't stare so stupidly!" The net effect -- the Verfremdungseffekt, or "alienation effect" -- is to force the audience to be active thinkers, not passive recipients of a storyline.
Realistic theater generally strives to create and maintain an illusion of reality throughout the performance. The sets may be simply, but they are generally treated as real, authentic spaces (such as the living room of Ibsen's A Doll's House). Like epic theater, realistic theater may have a strong message that it wishes to convey and a political agenda of its own, but it often also tries to reach the audience through emotional connections.
EDIT: Brecht's signs (see the link below) actually said "Glotzt nicht so romantisch!" or "Don't stare so romantically." My memory's not perfect, so I thought I had better check my facts.