In what some feel is a well-designed amplifier, with predominant 2nd Harmonic and ever falling higher harmonics, the distortion is very much alike to typical well-designed loudspeaker distortion.
Both can suffer from odd-harmonic distortions, but they are considered faults rather than attributes (when by "attributes" we mean what is preferred given that some distortion is inevitable).
The 2nd, 3rd and 4th harmonics are found in nature and in musical instruments, so getting the actual levels correct is less objectionable; odd harmonics are not, the ear/brain has elevated sensitivity to them and in general "dislikes" their presence.
What the exact correct 2HD 3HD and 4HD represent is the character of the instrument; two guitars from different manufacturers will have different levels of those harmonics, which musicians refer to the "tone" of the instrument. So maybe a Taylor sounds like a Gibson, or some similar confusion. They both sound like acoustic guitars though.
Speaker distortion is heavily skewed to lower frequencies; but consider that if the Low Frequency response of the speaker is limited (say, 60Hz at the same level as 1 KHz, and 30 Hz perhaps 12dB down) you are only hearing the 2nd harmonic of the lowest bass notes in any case; yet people tolerate that well.
