This is a tough topic to summarize, but I'll try. Check other sources for more detail - I've glossed over a lot of fine points here.
Let's look at how each species of amp handles a sine wave:
Class A, AB, and B are linear modes; i.e., the output is (more or less) proportional to the input signal. In Class A the amp stage conducts throughout both the positive and negative parts of the signal (360 degrees). Class A amp staged draw full rated current even at idle. Most of that comes back as heat. They are quite inefficient. All single ended amps are by definition Class A.
A Class B amp conducts only half of the cycle (180 degrees). The amp stage is off for the other half of the cycle. For audio use we need two class B stages, one for each half of the cycle. The two stages are driven out of phase. This is called push-pull operation. Class B is much more efficient than Class A.
The abrupt switching between the two stages of the push-pull amp result in distortion (crossover distortion). By letting each stage conduct a bit more than 180 degrees of the cycle we provide overlap and reduce the effect of crossover distortion. This is Class AB operation. Class AB is a bit less efficient than Class B but much more than Class A. Most hifi power amps are Class AB. BTW if I increase the overlap to the point where both stages conduct through 360 degrees of the signal then I have a Class A push-pull amplifier.
In Class C operation the amp stage conducts for less than 180 degrees of the cycle. For audio use this results in severe distortion as part of the waveform is clipped. Class C is normally used in RF transmitter output stages. These contain a tuned RF tank circuit that supplies the missing part of the waveform. Class C is non linear and not used in audio applications.
Class D is a non linear mode based on pulse width or pulse density modulation. The audio signal is converted into a pulse stream whose width or density is proportional to the signal. This pulse stream then controls output devices which are either fully conducting or off, depending on whether they are receiving a pulse. Some kind of low pass filter is needed to smooth the output and remove high order switching harmonics. Class D is very efficient.
So which sounds better? There are excellent examples of Class A, AB and D amps out there. Let me know when you figure it out!
Personally I run single ended Class A (Pass Aleph 1.2) monoblocks. The sound glorious, but draw about 600 watts from the power line at all times. They are space heaters.
