The Class of an amplifier is the method it used.
On a basic level, Class A/B uses two amplification devices, each aming half the input signal. These are then glued back together again. The can be crossover distortion (where the join is) BUT the signal is a true analogue signal throughout. Class D provides an apmplified on/off signal (hence why its sometimes called digital) triggered by the input - and then the OP signal is smoothed and shaped.
Early Class D amps wernt that great, and the OP waveform wasnt that smooth - good quality modern Class D amps are much better. The lower frequence the signal is the easier and better the smoothing - which is why its used a lot in Bass amplification and subs. Its also efficient an dcan be light - traditional Class A/B amps are heavier due to the cooling required and the power supply. Some modern Class A/B amps use different power supplies to reduce weight.
"general" opinion is that for audio (critical listening), Class A/B given the better result - though a great Class D design may be better than a budget A/B. Its also true that on a loud stage with a (hopefully) loud audience - your ot going to hear much (if any) difference. For being picky with your sound, in an otherwise quiet studio it may be different.
Ultimately the class isnt everything. Weight, size, output power required, cost all have a bearing in your choice - but everything else being equal I (along with most) would take Class A/B, however everything is very rarely equal.
