I think it would be difficult for me to just sit down with my system and distinguish two (new to me) SS amps that are very comparable build and spec. wise. However, I do think once you get some hours under your belt, its easier to pick out the differences in a fully treated listening area. Most people don't have any treatments, they have poor walls, bad corners, strange room shape and opening floor plans, bad speaker placement, etc. Getting the most from what you have is cheaper and brings more to the table than a quick and expensive component change. Treatment is everything and it took me 20 years to finally be convinced by it. Now, I can tell you its everything to my ears.
I ran a Fischer 100X2 SS amp and a old Onkyp pre that was all I knew back in the late 80's, hooked up to a pair of CW II's. I wish I still had those two components, just to let me know where I am today. I ran a first gen EMO XP5 or something like that through my modded K's from a fellow friend and the noise floor was so bad from the elevated input sensitivity it was literal insanity at idle and low level listening, but it sounded great on his Maggies. I also tried an Outlaw 5 or 7 channel amp many years ago, and it was an impressive and clean amp. I actually went to buy it after the audition and the owner fried it before I got there. I heard a pair of mono MC 30's back in the mid 90's hooked up to a pair of Heresy's at a friend of a friends house in Memphis. Let me say, this was one of the finest sounding setups I have ever listened to and I have never heard anything so lush. It wasn't analytical or even accurate, but it just oozed dreamy brass, vocals and just electrified the room. From Blues to Jazz, which was all he listened to, I was just floored by it. When my ticket comes in, I will own two sets of 30's.
Right now, I am running a MC7205 feeding K's up front and LS's in the rear. I set this up when the lossless multi channel audio was the big thing, and it still is in my book whether two channel or multi is involved. This amp is a bit cold and analytical, but extremely accurate and unforgiving. Is specs are off the chart in cleanliness, but you pay for this with the compromise of thinner SS sound. Its dead silent at idle and layers the content incredibly. I have called it good on this one, teamed up with a Marantz 8802a Pre. I know there are many, better multi channel amps out there, but I have slacked off from the hunt with my aging ears. I have heard many amps here and there, but you just cant give anything a fair shake until its sitting in your mix for a while. They all pretty much do the same thing, but the topography and components do change things up. Diminishing returns were mentioned earlier in the thread and that is a nail hit on the head after you reach a certain level of quality IMO.
Rounding back to the initial thread question. I think there is no doubt the majority here could listen to a intricate and/or delicate passage from one of their favorite artists they have heard for decades that they were familiar with, spending maybe 3-5 nights listening to actually hear differences to very similar built amps. However, if your room isnt treated or at least a halfway, you just might not. From the amount of Reverb and Echo I have previously had, I know I likely couldnt.