Best way to A / B test amps? Use a switch?

Constant switching will drive you crazy.  It is far better, IMHO, to listen to each piece of gear for couple of days to get feel what you like more.

Both approaches inform and have value.

@david_ten Yes, but comparing particular element, like bass or treble extension can result in choosing wrong gear.  In early seventies, before Transient Intermodulation Distortion surfaced, you could get a lot of amps with wonderful bass, treble etc, but sound of these amps was tiring over longer period of time.  When comparing such amp by switching, it would always win, but it was unpleasant to listen to on long run.

Running 2 systems myself. I build a switching unit with a break before make switch. It’s never a good idea to take a chance of accidentally connect 2 amps simultaneously. Something is going to give. Not hard to make and very cost effective. The switching is close to instantaneous. There are some switching units on the market you could try. Do not use speaker selector switches as the chance of having both amps connecting simultaneously is high in which case pop goes the weasel.  Break before make is the key phrase. 

@kijanki I’m in wholehearted agreement with you. I am also in wholehearted agreement with the "other" position and points made above.

I realize this (being in both 'camps' simultaneously) tends not to happen often in these environs.

I use both approaches. Each ’way’ can and does (though not always; and not always with certainty) offer unique and disparate information. This addresses non-overlapping areas of personal (human) interface and connection. Objectives for each ’approach’ focus on different natures / aspects.

Key (for me) is the overlay and the interlacing of the information gathered and how I use it to make a final decision and choice.