Fascinating discussion, and, as always, one of the most interesting topics. I agree, if we keep it civil there's no reason this can't be very worthwhile.
I think there's about three different things happening at once when you're trying to figure out for yourself whether or not you can hear a significant difference, especially between an inexpensive amp, a much more expensive amp, and (I love this one!) the OMFG amp.
As was pointed out (if I can remember any of my engineering statistics from too many decades ago) the level of chance guessing when listening to two different amps (or coin tosses) that you can't see is way higher than 50%. If a group of experienced listeners participate in a double blind test and guess correctly 60%, 65% of the time, that still does not indicate that a difference could be heard. The smaller the number of test points the higher the number will go, and vice versa, but it never gets down to 50% unless the number of test points goes to infinity.
Rich_Perry's comments pointed out another interesting issue...he knew which one he was listening to. I just read about another dbt using Coke and Pepsi, in which the test subjects had EEG's attached to their brains to read brain wave activity during the test. I forget the exact scientific explanation, but apparently the brain activity was markedly different among test subjects who had an opinion of which one they like the best while they were testing the two different drinks. In other words, they couldn't shut down their preconceived opinions even if they tried...it was kind of "hard-wired" in. If you already know which one is the expensive one and which one is the inexpensive one, it's impossible to eliminate that knowledge from the test. To use an OT example, if you're a tube guy vs a SS guy, you'll tend to go with what you already like.
Finally, the old "how much of your budget would you spend on different components" conundrum, i.e. you're not really listening to your amp, of course, you're listening to your speakers. Poor performing speakers won't uncover subtle differences between different amps, so there has to be an assumption that the speakers being used will have sufficient ability to "resolve" differences to be useful. In the same vein, Reyneman mentioned the very commonly held belief that the pre matters more, anyway. I think I lean that way, also. From a purely electronic circuit viewpoint, a power amp is (can be) a very, very simple device, with relatively few components, and does a very simple thing. Since it's the last point before the speakers (& cables) it certainly matters, but if you go back to the old computer GIGO thing, if it simply amplifies what it's fed (I think that's a low distortion comment!) then it shouldn't have a readily distinguishable affect on the sound.
If you have a nice system with a good pre and good speakers, and you swap back and forth between two amps with the same power rating and comparable THD & IM figures, I don't believe you will be able to hear a difference a statistically relevant amount of the time. Btw, this does NOT mean that I think specs are the most important thing. I don't. I believe they certainly matter, a lot, but I also believe there are things going on inside the brain in the area of psychoacoustics that are not clearly understood.
To sum up, once you pass a certain price/quality threshold (and I don't know what that is, but it isn't high) then the power amp is no longer the most important thing in your system, because you no longer will be able to hear changes in power amps as easily as you will be able to hear changes in preamps or speakers.
Ah, the first coffee buzz of the morning, and fingers flying over the keyboard!
Clay