Quality inversely related to power output?

only when they're grown from magic beans

There are few cases where larger amplifiers will sound better, all other things being equal. The disclaimer is important, since there are so many variables in amplifier design. The 'first watt' concept has a lot of credibility, since in many cases the amplifier will be making less than a watt most of the time. Most of the power is used on peaks.

In tube amplifiers the size of the output transformer is paramount. The issue is getting full bass performance vs HF performance. This is challenging and you can assume that any high powered transformer-coupled tube amplifier will have limited bandwidth.

With SETs this issue is even more pronounced and is why the ones that are 7 watts or less are also considered the best sounding. Time was that the 300b was King, 5-7 years ago the 2A3 took ascendancy (about 3.5 watts) and nowadays you hear an awful lot about 45-based amplifiers (maybe about 1 watt).

OTLs do not have this issue; IMO/IME the bigger you make them they better they sound. As far as I can tell this is the only amplifier technology for which it is true that bigger is better.

With transistor amplifiers the issue is all the paralleled devices, which will 'hog' current to a much greater degree than paralleled tubes will. Thus its pretty much mandatory that in a larger power amplifier, all the output devices are matched. Another issue you get into with larger power amplifiers is the extreme levels of negative feedback that are employed- such designs rarely bring home the bacon insofar as the rules of human hearing are concerned.

All this points to the efficiency of the loudspeaker as being quite important overall- since truly musical high powered amplifiers are nearly oxymoronic in general, one will always be challenged to get low efficiency speakers to sound like real music.

All this points to the efficiency of the loudspeaker as being quite important overall

However, this now requires "all other things being equal" in speaker design. It is generally not as easy to find a full range speaker of 100+ db SPL with acoustical performance that is competitive with the many speakers designed between 85 to 91 db sensitivity. (Generally designers equalize drivers downwards to achieve a desirable acoustical performance (crossovers etc.) because the raw driver output is rarely flat and smooth on and off axis acros the frequency range.

The rule I use is to use the smallest amp that will do the job. For example, when I decided to buy a Musical Fidelity integrated amp I had a choice of 4 generations with each generation having more power and more output devices. I chose the oldest and simplest one because although it had the lowest power it still had more power than I would need. But a choice like this is seldom available. I have been looking at the C-J 350 transistor amp. They do not make a comparable lower powered version of it. So it all depends, but if the lower powered amps in a range meet your power needs and they are of comparable quality with the more powerful I would go with them.

In some cases a manufacturer offers two amps with different power ratings, and the only difference is the "rail" voltage (which means a different power supply). Sometimes, but not always, the output transistors may be a different type. But all the input and gain circuitry is the same.