Is powerfull Amps only for low sensitivity speakes?

I can only give you my experience which is a reflection of what I believe Koost is saying. In short its about synergy. IME, my low powered systems have sounded better. IE, I had a Conrad Johnson MF2500A (250wpc) paired with a CJ PFR preamp.It sounded good with my Silverline Sonatas 93.5db. But I got an urge to try tubes. So I bought a fully modded Dynaco ST-70 just to dip my foot in to see what all the fuss was about for tubes. Its a mere 35wpc. Guess which amp kept?
Another amp which shined brightly in my system in the late ’70’s was a Harmon Kardon 45wpc Solid state. It was paired with large Advents and later Infinity RS series, both 89db (I believe) 

2. Is there any *disadvantage* to powerful amps with efficient or small speakers? No.

There is nothing about a powerful amp that is inherently a compromise of sound for power

These statements are not accurate. If the amp makes too much power and the speaker has no need for it, the amp will be operating in a lower power region. With most higher power amps, this means it will have increased distortion. You can see this in their specs. The increased distortion is audible as brightness in most cases and will result in less detail as the distortion will mask lower level signals.

@obatu Your speakers are only 92db; that is a moderate sensitivity- high sensitivity would be more like 98 or 99 db at a minimum. An amplifier of the power you mention will be no worries.

Just look at the Audio Precison graphs at different power output levels of a 2x350 watt Yamaha p3500s pro audio amplifier: http://www.homecinema-fr.com/forum/amplificateurs-de-puissance-haute-fidelite/mesures-ampli-yamaha-p...
It is true that distortion goes up a little bit at lower levels, but it is still very low and below the noise level: 0.05% at 100 mW. Look at graph 16 in particular, for the output range of 480mW to 7.7 W rms. In that range it never gets above 0.015% and rapidly descends to 0.01%. There is no way you can hear this.

It is true that distortion goes up a little bit at lower levels, but it is still very low and below the noise level: 0.05% at 100 mW. Look at graph 16 in particular, for the output range of 480mW to 7.7 W rms. In that range it never gets above 0.015% and rapidly descends to 0.01%. There is no way you can hear this.

Sure you can- if you have high sensitivity loudspeakers!

What you are not taking into account is the nature of the distortion (mostly higher ordered harmonics) and the fact that the human ear uses the higher ordered harmonics to sense sound pressure. We are more sensitive to them than almost anything else! So they manifest in amounts this small as brightness. This is what has fueled the tubes/transistor debate for decades.

But a powerful solid state amplifier allows you to use mostly far better inefficient speakers and avoid the distortion and non-flat frequency response of many tube amplifiers. Anyway, we are not going to persuade each other.