We can easily distinguish changes in loudness but human beings are not SPL meters - our sensory system doesn't work that way in the sense of being able to calibrate what we hear in dB - cue the eleven is one louder sketch in Spinal Tap.
As regards the reference to amplifier power in the OP. I don't think many people look for more powerful amplifiers from the perspective of playing louder. It's more about dynamic range and playing at the desired volume level without distortion.
Speaking of distortion, a low wattage amplifier driven into clipping will sound subjectively louder than a high power amplifier playing at equivalent or lower SPLs.
As another example, modern popular music which has been compressed to hell sounds superficially louder - hence the loudness wars in modern mastering.
So loudness is a bit of an ephemeral concept.