How important is it to match amplifier power output with speaker sensitivity?

Very important. This combination of technical parameters determines the actual sound pressure level you can attain without distortion and also tells us a lot about the dynamic capabilities of the system. As usual, the answers lie in physics rather than opinion.

For example, let’s say you have a low powered amplifier, say something up to around 30 Watts per channel. To achieve realistic dynamics and sound pressure levels, you’ll need sensitive speakers, over 90dB/Watt sensitivity, preferably a lot more, to be able to play loudly, with realistic dynamics. If that amplifier is matched up with speakers with relatively normal sensitivity, the result will be a system that sounds strained and lacking in dynamics at anything but very low levels. It can work, but only just, and in the right context, ie mellow music, small room, no desire for realistic sound pressures.

Conversely, let’s say you have a very powerful amplifier, something like 300 – 500 Watts per channel or more. This gives you a lot more room to move and means you can use speakers down to really relatively insensitive 83 to 85dB/Watt. This gives you more choice and allows crushingly high sound pressure of course with speakers of 88 – 90dB/Watt sensitivity or more. It also gives you great dynamic range and headroom.

Is one approach better than the other? Not really, they both have merit. I use a very high powered amplifier (500 Watts/channel) on the end of relatively normal sensitivity speakers. This allows for a good mix of everything, microdynamics, massive sounds pressures if needed etc. I’ve also heard amazing sounds from super low powered valve amplifiers like say 7 Watts/channel, and super sensitive horn speakers at around 100dB/Watt. What you don’t want is a low powered amp on the end of not very sensitive speakers. This is always bad!