More power, more better when comparing apples to apples is pretty spot on. The best example of this I’ve ever heard is when I added a second Devialet to my system go from a 200 to a 400. It was an instant wow. Same technology all around, just more power. 
 

But now I use a Luxman 590, 30w class A and will never go back. 
 

The type of power seems to me to be way more important than the amount of power. 

Some amps with a lower rated power sound more powerful than their specs would have you believe (due to good design and a robust power supply). Speaker sensitivities are unreliable (and misleading). If a high powered amp sounds “more dynamic” than a lower powered amp at lower levels, it is not due to its maximum power rating in watts, it has much more to do with the amp’s design, regardless of rated power. An amp’s input sensitivity dictates what sound level will be produced at what position of the volume control (all else being equal). If you listen to music at moderate levels, you likely don’t need as much power as you think you do. I’m getting some of the best sound of MY life with a Music Reference RM-10 amp (35 w/ch) driving my Magnepan 3.7s… and I’ve used dozens of amps of various power ratings over the past 37 years (I’ve always had Maggies in the house).  This is my experience with power. Ymmv. Gotta try some different amps out with an open mind regarding power!

Understanding Amplifier Power Output Specifications

Don’t base an amplifier’s quality just on its wattage output

@mulveling wrote:

... When dealing with say L/R channel imbalances, you can certainly notice down to a third of a decibel, at least.

Indeed. My Xilica digital crossover/DSP has gain adjustment in 0.25dB increments, and occasionally I wish 0.10dB increments had been available.

@2psyop wrote:

What is you experience with high power, high current amps ? Do your speakers sound better with more power? At low volumes, in a small or medium sized room? Do you think the quality of the music is dependent on higher powered amps?

My previous, passively configured speaker setup (104dB sensitivity) had a 30W class A power amp delivering substantial SPL output with ease, where my current, actively configured speaker system is powered by a combined 2,350W per channel with a sensitivity range of 97, 100 and 111dB’s (subs, midbass and HF/MF horn). Even with high sensitivity in both speaker cases the latter, active scenario lets the prodigious power wallop at hand here shine through at moderate as well as very high SPL’s, but that’s just speaking of the perceived power envelope in different contexts. Perhaps more relevant would be comparing different power scenarios via one and the same speaker combo and (preferably) the same amp brand/series, which I have, and with my current, active speaker system and chosen amp brand/series this has yielded a slightly more assured and fuller presentation with the more powerful iterations from the same series (even with a very slight difference of 575 vs. 625W/8 ohm). Rarely using more than 10-20W in my specific case this may seem an improbable outcome, but listening soon lets one know otherwise.

I’d say it is more the speaker than the Amp. I’m running only 30 watts of class A power into the Tannoys... (Sugden A21se signature)plenty of power! They are honestly the best speakers I’ve heard at low volumes...still sound full and I do not feel I have to play them loud, as it is still all there