"Hearing The Music Of Pnimiyus Ha-Torah"
Rabbi Dovid Sears commenting on "Others Admitted It Was Lost"
I agree with most of A Yid's analysis. However, there may be something to the "ChaGaS" rubric if we understand it as applying to the external, social formula of Chassidus instead of the internal, individual-oriented derakhim in 'avodas Hashem.
Most Chassidic communities after the period of the talmidei ha-Maggid and even more so after the Tzanzer Rov relegated the deeper parts of Chassidus and pnimiyus 'avodah to their Rebbes and certain yechidei segulah, while ChaBaD sought to use the intellect as a vehicle for hasagas Elokus, and to involve as many kinds of people as possible in this lofty enterprise. (As A Yid pointed out, Breslev, Ziditchov-Komarno, Izhbitz-Radzyn, and Piacetzno are among the several major exceptions to these classifications.)
However, the derakhim of the great Rebbes and "baalei machshavah" as individuals speaking to other searching souls are very complex and diverse, and can't be simply pegged as "CHaBaD," or "ChAGaS," or "NHYM," either. Ultimately, each tzaddik "hears the music" of pnimiyus ha-Torah his own way and tries to communicate it to those who share his shoresh ha-neshamah.