What’s the relationship between gain (dB) and power (watts)?

The practical difference is about reducing noise thats generated from the pre - amp feeding the amp. A pre-amp with a high output signal may deliver unwanted hum or hiss when the input sensitivity switch is at the higher setting. Along the same lines, if really efficient speakers are being used residual noise from the pre-amp may be audible; flipping the amp input switch to the lower setting will tend to reduce the noise. 

My Question:
Setup is active speakers and pre-amp.
Speakers have input gain knob for -10 to +10 db.
Which is best, crank the volume on the pre amp upto 80% or add gain on the speakers and less on the pre-amp.

Btw. Pass XP-22 and Adam Tensor Delta  speakers

That Bryston gain switch would be to match the volume of two disparate amps on the same preamp.

MC running a clinic here. Nice. 

A master clinic involves the recognition that in power amps variable gain is just variable negative feedback. See Roger Modjeski for an EE w ears and many successful designs the variable NFB RM-9 being a sonic master class. The cool thing about variable NFB w time and phase accurate speakers is that the intrepid listener ( given a decent recording ) can discern how NFB effects image depth....
carry on....
see also Burning Amp