Amplifiers are usually specified for distortion at around maximum power. Low order non-linear distortion increases with increasing output power, so max power is the 'worst case' place to measure it. Both tube amps and solid state (SS) amps suffer from this, though tube amps have rather more. A modest amount of low order harmonic distortion can sound relatively pleasant and 'warm', often adding something 'extra' to the music, so the high distortion from tube amps is not generally perceived as a vice.
When they go into overload, SS amplifiers 'hit the rails', whereas tube amps 'go a bit further round the corner'. Needless to say, the former sounds nasty, the latter can often be forgiven. This means that for equivalently rated tube and SS amps, the tube amp is more tolerant of mis-set levels.
Push-pull class B output stages on SS amplifiers have another distortion mechanism, cross-over distortion. This type of distortion tends to be independent of output power, so in ratio terms is worst when the output signal is small, just where you'd expect the amplifier to be performing best. This type of distortion tends to be high order, so is un-musical , harsh, 'wearing' and generally not liked.
Unfortunately, many of the first SS amplifiers to be made commercially available were very bad for crossover. A quite passable distortion level at full power of 0.1% on a 100W amplifier could become 3% when outputting 100mW. Although rock tends not to have these dynamic ranges, classical music does, and musicians hated the violence that was done to delicate passages on a few instruments.
Designers rapidly improved the design of output stages, improved the stability of biassing with respect to temperature, and got crossover distortion under control at all output levels, but by then, SS amplifiers had already got a very bad press. This was made worse by a) there were already a large number of amplifiers out there and b) bad ones were still being built and sold as the design knowledge did not pass quickly from the good to the bad manufacturers.
As music is such a subjective personal experience, it's difficult to correlate enjoyment with audio fidelity. With large sums of money to be made catering for the luxury end of the audio market, the less scrupulous manufacturers have little incentive to disabuse the buyers. It's well known and demonstrated in tests that music sounds better when there's a shiny tube amp glowing on the counter, than when there's a non-descript black box there, whatever is producing the sounds.
A personal anecdote on the musical effect of low order harmonics, which I'll try to keep brief. When I first started my music collection as a student in the mid '70s, I had little money, so first bought a decent deck and cartridge, so as not to damage my record collection, and listened with emitter followers and headphones. Next year, I built the Practical Electronics 'Gemini' 50W stereo amplifier, but initially could only afford a couple of tiny 3W car speakers from a jumble sale. Nevertheless, Annie Austere from Fruupp's Prince of Heaven's Eyes sounded glorious, huge swathes of big sound, a chorus of ... you get the idea. Listening again, the effect is rather like much of Quadrophenia!
Two terms later, I finally built my KEFkit IIIs, in 120 litre cabs. Now I was going to listen to that track the way it should be heard. It sounded OK, so I turned it up. It still sounded OK. I turned it up some more. Eventually, the windows were rattling, my ears were hurting, the neighbours were complaining, and it still sounded OK. The technicolor swathes of glorious sound had been the distortion from my way under-powered speakers. Sigh!