How do Brecht's and Ibsen's approaches to themes, narratives, and performance techniques compare?

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.

What is the difference between Brecht’s and Ibsen’s styles of drama?

Ibsen is usually used as the model for domestic realism, in which characters are depicted realistically, well within the psychological bounds of reason, acting out their domestic problems in domestic settings, whose symbolic connection to social inequities, etc. is implied but subtle—Nora Helmer or Hedda Gabler are believable characters in their familiar domestic surroundings.  Brecht differs from realism in two important respects: first, he is more interested in political inequalities and problems than simple domestic ones.  Thus, Mutter Courage und Ihre Kinder (Mother Courage and Her Children), while superficially dramatizing a domestic problem, is actually dramatizing the larger problem of war, especially its connection to commerce.   Second, Brecht never wants his audience to forget that they are in the theatre—an opposite motive from the realism of Ibsen, who wanted the audience to believe they were in the Gabler house, etc.  The method Brecht used to distance the audience from the performance—exaggeration, breaking into song, costumes and dialogue to one side of the ordinary, etc.—was given a name—Verfremdungseffekt – meaning alienation effect. So the political message and the non-naturalistic dramatization separated Ibsen from Brecht.