How can I compare Brecht to Ibsen, with respect to their approach to the main theme of their plays, the development of their narratives, performance techniques, etc.?

In terms of the elements of technique you have listed in your question, I would say that Brecht and Ibsen have little in common, except that there is a tenuous similarity between their approaches to the themes in their plays.
Both men were iconoclasts in their thinking, and in their plays they present a reevaluation, or an overturning, of traditional attitudes about religion and society. Ibsen was ahead of his time in dealing uncompromisingly with gender issues, not only in A Doll's House, but in Hedda Gabler as well. He also tends to champion the individual who resists pressure to conform to society's demands, as in Enemy of the People. Bertolt Brecht was a progressive in these same areas of thought, but with the major difference that he promoted a Marxian view of societal issues. Often the message of a Brecht play seems deliberately planned to fit into this Marxian mold. In The Caucasian Chalk Circle, for example, the theme is basically that land should belong to those who can "use" it properly, without reference to other factors traditionally in play with regard to ownership.
Much of Brecht's work satirizes capitalism, in an impudent, ribald manner, such as in his works written in collaboration with the composer Kurt Weill: The Threepenny Opera, and The Rise and Fall of the City of Mahagonny. Henrik Ibsen, on the other hand, wrote independently of any specific ideology, though Brecht seems to echo Ibsen's themes at times.
In terms of narrative technique there are huge differences between Ibsen and Brecht. Ibsen is a realistic playwright. His stage action and dialogue conform to "real life," and one has the feeling that his characters are people one could meet in the everyday world. Brecht is a modernist. His technique involves fantasy-like shifts in time and story-line. In The Caucasian Chalk Circle there is a play within a play, narrated in a fable-like manner by the Singer. Brecht also explicitly promotes a technique known as "alienation effect," in which he deliberately wishes the audience to be "distanced" from the emotion and the thoughts of the characters on stage. Critics often cite his Mother Courage and Her Children as an instance of this effect not being carried out successfully, as it's impossible not to feel sympathy for Mother Courage at the end of the play. In general however, and unlike in the realistic theater and fiction of the nineteenth century, in modernist works such as Brecht's plays and the Theater of the Absurd the audience or reader is not supposed to "engage" emotionally with the characters and situations. Brecht, unlike the absurdists, is a didactic writer who wishes to impart a moral lesson. But his works do so in a completely different way from those of Ibsen a half century earlier.