When it comes to adjusting for the 'musicality' of distortion, it's very much a matter of personal taste of course..... and discussions on which distortion is preferable to create the 'best' sound can get very agititated !
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Distortion is of course anything that introduces non linearity into the signal path.... That might be deliberate (or accidental!) changes to the frequency response, or perhaps different characters of overload distortion introduced by different bias adjutment?... Not forgetting the 'nice' distortion that many transformers are said to add!
I have to confess, at the moment I'm tending towards using op-amp impedance converters, which are very linear and can have high maximum signal level outputs. They do tend to produce a very 'clean' signal.
That then gives the opportunity to introduce any desired 'non linear' effects into the signal path outside the microphone -- channel strip compression, EQ, soft clip diode limiting, de-essing etc etc....
Flexible options which can be carried out at line level, making the the problems of adding unwanted noise by introducing effects early in the signal path much less likely ...
But we all have our own favourite ways of doing these things!