Essentially, BASH is an analog power stage fed by digitally controlled power-rails. Its switching power supply continually varies the power-rail voltages according to the audio input signal, so that the rail voltage is always barely above the amp's output voltage swing. This greatly reduces the amp's power consumption, allowing a greater power output in a given package size. It is certainly a suitable amp technology for powered subs, in which the inevitable high-frequency noise coming from the digital power supply is much less of an issue.
BASH is not inherently superior or inferior with regard to sound quality compared to conventional analog power amps, except that it can achieve greater power output in smaller size.
