The Previous Lubavitcher Rebbe expressed the power of a Chassidic niggun in the following manner:[1]
A standard Chassidic Niggun uplifts the individual 3 handbreadths above the corporeality of this world. A niggun of a rebbe, uplifts the person higher still, but the distinctive niggun of the Alter Rebbe uplifts the person to the greatest of heights.
The meaning of the concept of greatest of heights, is that the intellect is expressive in one’s G-dly service.
[1] Sefer HaMa-amorim 5710, Pg. 246