I've followed the debates on tube amps for many years and not being an electrical engineer I'm not qualified to determine the answer.
But from what I've seen the answer to why tube amplification can be preferred by some is far from easy or established. First there's the problem of whether in any particular case, someone is actually able to hear a difference, that is if the distortion is audible, or if he is imagining it.
Then if it's granted that audible distortion is occurring, it's still vexing. The usual folk lore is that tube amplifiers distort in a pleasant way, both in clipping behavior and in the harmonics added in the distortion "primarily pleasant sounding 2nd order harmonics that can slightly thicken and brighten the sound." The problem there is that this may indeed explain *some* tube amplifier distortions, e.g. some single ended triode designs that people use to run high efficiency speakers. However plenty of tube amps, e.g. push-pull designs, seem to produce some odd order distortions just as solid state is *purported* to produce as well (though very low level). So it starts to become a head-scratcher - at least to laymen like me trying to follow the debates - as to what exactly if anything is causing the "pleasant" distortions when they occur. Some lay the blame on the tube amp output transformers. I dunno.