When the pickup output signal is amplified without tonal modification (bass, mid or treble boosts or cuts) and with the least distortion it is "unflavored", so to speak. As long as the distortion level remains below approximately 0.005% (Total Harmonic Distortion and Intermodulation Distortion) the signal is being amplified "cleanly" regardless of what type of amplification is used (tubes, transistors or FET's, in or out of op-amps). It is difficult for tube circuits to attain or exceed these performance specifications. And so there are many "flavors" of amplification all of which are distortions of the original signal. Accurate amplification should be simply "transparent".
Once tonal modification (spectrum shaping in the form of bass, mid or treble boosts or cuts) is introduced then phase distortion comes into play and each equalization system will have its own "flavor".
The differences become larger as the signal grows beyond the "linear range" of the amplification system (where the input is proportional to output) and the distortion level increases.