More SPL = more perceived bass, though, which is an important source of these misconceptions. When comparing amplifiers without accurate level matching, the setting of volume controls is likely to be biased towards equal volume control position, therefore the more powerful amp with (typically) higher gain will be louder and sound "better".
More SPL = More SPL. It doesn't = More or Less Bass. I get the "perception" notion, but you would seriously have to be a bit of a dummy not to notice that loudness was different and assume it had nothing to do with the volume knob!
Level matching amps for comparison sake is good practice. But if a "more powerful amp" with a "higher gain" sounds "louder", well then, guess what? You apparently haven't level matched! If you had, Amp A and AMP B would be producing the same SPL on the same Speaker, and the user could decide if there was a difference in the sound. Then they would feel stupid for buying the amp that had a wicked High Gain and clipped at home, or which, driven hard, produced enough "power" but was also distorting.
More Power = More SPL.
If the speaker can take it, and the user wants it, more power = good. But Amps serve a utilitarian purpose FIRST and foremost. More Power does not = more bass. Most people don't realize that they probably only use a fraction of an Amps rated power at any given time. Volume is lower, but "bass" is exactly as it should be.