There is an AES Paper ... somewhere ... that describes listeners preferences, and listener fatigue.
The short answer is ordinary, untrained listeners tend to prefer the slightly bright amplifier with high order distortions for about one hour, at which point they no longer wish to continue listening. After that one hour period, they then tend to prefer the amplifier that exhibits low levels of high odd order harmonic distortions.
Then there was the demonstration at RMAF by Audio Precision (the company that manufactures the better distortion analyzers) where they played back music to panels of show-goers with specific introduced harmonic distortions. Audience members were asked to raise their hands when the sound became objectionable.
For high order odd harmonic distortions, the majority of listeners raised their hands with relatively low distortion percentages, and the entire audience had raised their hands at levels around 1%. When second harmonic and third harmonic distortions were the added components, audiences were able to tolerate significantly higher levels; for second order some members didn't raise their hands until the level reached 30%.
Taken together, there is much evidence that the harmonic profile is critical to listener enjoyment.
The amplifiers that I first noticed I enjoyed over most of the competition, forty years ago, was the Luxman tube amps and the Threshold 400A.