I'll share my experience. Along with a pair of Legacy Audio Focus speakers which are low to mid 90's efficient, I was using a Plinius SA-103 power amp that delivered 125 watts into 8 ohms and 220 watts into 4 ohms. I always felt that it lacked a bit of power and indeed there were times when listening at high volume levels during a sudden transient, it would go into protection mode. I decided to sell it and replaced it with a Plinuis SB-301MKII which offers 310 watts into 8 ohms and 470 watts into 4 ohms. The improvement was amazing. I had a much deeper dynamic range now and everything sounded more balanced across the frequency spectrum. I have never driven this amp into clipping or protection mode and I'm afraid to think what it would take.
In contrast in my second system, I am driving Legacy Audio Signature III's with a small Plinius (yes, I like Plinius and Legacy together) 9100 integrated rated at 120 watts into 8 ohms and it drives them with authority. I recently picked up a small EL34 tube amp that puts out a whopping 8 watts for another project. I hooked it up to the Signature III's and was amazed at how good it sounded......with the right music! And there is the rub! When playing a cut from say, Passenger with an acoustic guitar and vocals it has plenty of power and can play loud. In contrast switching over to a London Grammar track with lots of deep bass, you can hear the tubes go into clipping easily. As a matter of fact, it can barely play some of their tracks.
So my conclusion is, the more power the better except in some circumstances where you may be listening to acoustic music or light jazz then you can get away with less power. The key to each of the aforementioned amps is current and power rating together. I would never drive high efficiency speakers with high power however so there are always exceptions to the rule.