Typically, after one quick switch to hear note any obvious differences. I’ll put the new amp in for a week and try not to "listen to the amp", just the music. Then I will switch. Do this a couple times and the differences in gestalt and details will become clear.
Rapid back and forth changes... with all the physical stuff in between will erase any memory you have of the music you heard before. Professional dealers have done enough A-B ing that they may have developed a better sense than most of us normal people. Besides there are dozens of aspects to the music... so you can only hold a couple during quick changes. Experienceing and learning the differences in amps requires time and lots of different musical types.