I'm very impressed. You've played through more than a million amps? that's more than 1'000'000'000 amps? Impressive indeed. The reason why your solid state amp sounds different through 4 vs 16 ohms is that the amp is delivering more power when connected to a 4ohm load (solid state amp deliver the same voltage regardless of load and the load draws current, hence the increase in power). Because in 4 ohms, there's more power, its slightly louder and with more loudness, your ears will hear things differently. If you ran your amp louder while using the 16 ohm cab, the sound would be identical. If the claim was made with a tube amp, I would say that its the placebo effect. Same speakers, same power output, same dispersion, same tone.