Well, as most things in life its rarely that simple.
I have found that more power does tend to mean that things sound less strained and more dynamic when you do turn the wick up. Its not really about maximum SPL levels because you need to double power to increase by just 3dB. To put that into context generally people consider an increase of 10dB to sound twice as loud. For reference disconnect one of your speakers, that is now 3dB quieter.
Also speaker sensitivity has a *big* impact. As mentioned above double the power is required to increase SPL by 3dB. So an 85dB/w/m speaker needs twice the power to sound as loud as a 88dB/w/m speaker.
Another consideration is the parameters of the speaker load. If it has extreme phase angles the amplifier has to cope with dissipating (wasting) far more power than is being usefully used in the load.