Given your statement, at what decibel level do you consider the volume
to be something "higher" than lower volume? The essence of the question
is at what power level do tubes no longer "rule" over SS because of
power concerns. Thank you.
Its not so much a decibel thing as it is a distortion thing.
Take a look at the distortion curves of a typical solid state amp. At a certain lower power level, the distortion is at its minimum and as you go to lower levels the distortion can be significantly higher! This is not a given with tube amps, even push-pull amps (our amps are push-pull but distortion linearly decreases to unmeasurable as power is decreased).
So that power level is about 5-7% of full power with most solid state amps. If you've ever heard that bit about the 'first watt' being the most important, that's because its all about distortion (or in this case, the lack of it). BTW, Nelson Pass has a set of solid state amps called the 'First Watt' amps and they are so-named because they diverge from the usual solid state amps in that they too are very low distortion at low power levels. Their designs are also quite minimalist (even simpler than and not unlike tube amps in that regard) although they don't make a lot of power.
If you want good resolution so you hear everything (including good bass) at lower levels, this is what you have to do: tubes or a low powered solid state amp like a First Watt.
Now to the latter portion of the question- even at high power levels, the presentation continues to be all about distortion (or the lack of it). The thing is, the ear weights certain forms of distortion over other forms. What I mean by this is most people understand that the ear hears sound pressure on a logarithmic curve. What is considerably less understood is that the ear also detects harmonics on something that looks like a log curve. It is far more sensitive to higher orders (in particular the odd orders) than it is to the lower orders like the 2nd or 3rd harmonic. For this reason, we tolerate large amounts of lower ordered harmonic easily, but don't tolerate higher ordered harmonics well at all.
Audiophiles have terms for trace amounts of higher ordered harmonics; 'bright' and 'harsh' are common examples. This continues to be the big difference between tubes and solid state with regards to distortion! Now think about that weighting issue I mentioned: essentially, solid state amps have much **greater** amounts of distortion if you weight the distortion according to how the ear/brain system responds to it (all forms of distortion are converted to a tonality of some sort BTW). So a 7th harmonic at 0.005% is a much bigger sin in terms of coloration than a 2nd harmonic at 1%. Its a bit of an inconvenient truth.
Our measurement and testing regime is a good 40-50 years behind our understanding of physiology at this point, which is why there is still a tubes/transistors debate going on in high end audio.