input sensitivity

An amp with high sensitivity is more prone to noise pickup in the interconnect. I prefer to boost the signals to a good high level before sending them through my (admittedly long) interconnects. However, with good wire and good electronics noise should not be an issue, but the oversensitive volume control, mentioned by Aball is a problem.

in addition amps with high input sensitivity have limited dynamic headroom.
powerfull amps usually need >2V input voltage to reach full output power.

The input sensitivity of the CarverPro ZR1600 that I use can be changed by moving a jumper plug between four positions.
0.316 vrms...common in consumer electronics with low voltage unbalanced outputs.
0.775 vrms...most common line-level calibration.
1.23 vrms...commonly seen in professional audio products with balanced outputs.
2.45...Devices with large voltage swing used to drive long line-level paths.

These signal levels produce full output: 600 watts into 4 ohms. I use 2.45 vrms.
The descriptions are from the owner's manual.

Great thread and answers. Input sensitivity has been discussed often on the 'Gon, but there's a lot of info in the responses here.

I've noticed what Aball mentions about higher sensitivity amps sounding more full-bodied, but had always chalked it up to the sonic character of the amp itself.

That said, when I was comparing five amps around three years ago, I noticed that the BAT VK200 sounded much more full-bodied than the Bryston 4B in my system. The BAT also needed less volume adjustment to play loud. The BAT has an input impedance of 100k ohms while the Bryston I believe is around 50k ohms. It is interesting that in this comparison the Pass Aleph 3 which has an input impedance of only 23k ohms suffered greatly in its ability to play loud, reproduce bass and in general drive my speakers. But despite all this it still managed to have a full sounding midrange especially in comparison to the Bryston.

Could it have been a combination of impedance matching, system dynamics and the personal characteristics of the amps at work here?

Unless you were using a preamp with a high output impedance, I think it's unlikely that that the input impedance differences between those amps are the reason they sounded different. (Input impedance is different from input sensitivity.) The Pass is much lower-powered than the other two and doesn't have the best bass but does have a rich midrange. Its low input impedance can be a mismatch with some tube preamps, theoretically at least.