Feel free to augment or quibble, but I would call an "objectively
audible difference" between amplifiers as follows:
when the equipment is gain-matched to be sure the difference is not
simply due to different overall volume levels, listeners can still
repeatably distinguish between different pieces of equipment *only by
listening*.
OK- 'objectively audible difference' sounds different (if you will pardon the expression) from 'objectively audible'; thanks for clearing that up.
The thing that bothers me about this sort of approach is that usually when I see or hear someone talking in this manner, they are usually only allowing for certain circuits (amplifiers) to be in the conversation, while out of hand rejecting others on an arbitrary basis.
The problem is that in high end audio, there is a community of designers that take different approaches to solving amplifier issues. Some of them are quite brilliant and their works stands easily on their own merits, such as David Berning or Nelson Pass and there are many more. Further, a good number of designers including those I just mentioned, are not completely convinced that they should be using amps with ultra low output impedances (which means that their amps may not act as perfect voltage sources either). In my case, I've avoided making our amps work as voltage sources with intention- as I see the approach as highly problematic. Chief among these is the well-known fact that in removing distortion, the operation of negative feedback adds some of its own, which is always audible as increased brightness and harshness. I'm not saying its bad but I am saying that most of the time its inappropriately applied or inexpertly applied, with a mediocre result, which I see as about 95% of all traditional amplifiers made.
Now the approach I take is nothing new- its what was around prior to Mac and EV developing the voltage rules that are used today. Most people don't realize that there was something before that! I'm by no means the only one doing it either- and in all cases the idea is simple: the ear will place a priority on tonality created by distortion over a tonality created by FR error. To this end, a system that has less audible distortion can sound more neutral than one that has flatter FR. You have to be pickier about the amp/speaker interface (which is what the voltage rules were designed to prevent) but it can pay off in spades, but DBX people don't like to even consider such an amplifier in a DBX trial.