Schoenberg intended that the various manipulation of the prime tone row (inversion, retrograde, retrograde inversion, transposition) into the various 48 permutations would be perceived as modulation to a different key. Even Prof Robert Greenberg who thinks Schoenberg to be a great composer believes that he was incorrect with that assertion and that Schoenberg was only able to make the tone row so-called "modulation" perceivable due to phase structure, timbre etc and that changing the tone row can not be perceived as modulating to a different key can be. By judging 12 tone system by the standards of the original creator, Schoenberg must be the greatest failure in classical music (even if people can argue that succeeded in different ways that is unrelated to the original intent)
If there is any perceived diversity in a 12 tone technique it's due to elements completely unrelated to the tone row. Maybe the prime row is played forte, maybe the retrograde inversion is played pizzicato string, perhaps the prime +4 transposition has a crescendo, perhaps the retrograde inversion + 7 is presented as a fugue. Those perceived diversity and different section of the piece is due to the dynamics, timbre, instrumentation, form rather than the tone row itself. Making a retrograde inversion of the tone row will not change the mood of the piece akin to modulation to another key signature will.
Although I haven't heard Berg - Chamber Concerto, Alban Berg serialised works is probably more listenable than other serial composers as he organised the tone row to mimic tonality. He structures his tone row so that he creates triadic pattern so that we perceived the piece has tonality even if it doesn't have it. For example I could have the first three notes of the tone row to be C, Eb, G hence a C minor chord. I could end the tone row with a E and then A hence have something akin to a perfect cadence in A minor to closed the tone row paragraph. That's why Alban Berg work is probably the most accessible out of all the serialised composer.
However if the argument that 12 tone technique can create listenable music because you can mimic tonality within the tone row is not really the greatest argument supporting 12 tone technique. I mean if 12 tone technique is only listenable if you mimic the rules of tonality, you might as well write tonal music.