I have designed class AB power amps with SMPS and conventional power supplies, and with the same amp design, the difference between the two supplies was not at all easily noticeable. This was with the NeoPak 3.5 and that convinced me of the future of SMPS. The SMPS was designed to emulate the characteristics of a traditional supply, but that wasn't a big deal. The point here is that the supply was the only difference.
So, identical amps with different supplies and the results were that the differences were very, very minor. Perhaps trivially so.
Well, we never compared our class A/B with with two different power supplies, but I would agree with your opinion on the power supply. In our listening test we tried four totally different power sections, two class D, a class H and a class A/B, mated to the same preamp. In that instance, there was a very noticeable difference in sound and feel between the various topologies. There were no measurements taken and no frequency analysis done. I made the final choice for our amp strictly by ear.