The sonics of power supplies are different for SE and PP amplifiers, so it is impossible to generalize without specifying the amplifier topology.
The modulations of supply current on the main B+ supply in a single-ended amplifier are simply the music itself, with an addition of noise from the rectifier stack. Single-ended amplifiers are entirely Class A in operation, by the way.
This is not true for a balanced or push-pull Class A amplifier. The modulation of music on the supply is reduced by 30 to 35 dB (depending on balance), and what’s there is doubled in frequency, similar to a balanced-detector in a radio. The balanced-detector artifacts are the result of symmetric nonlinearities in the balanced pair ... if they have 100% distortion, you get a balanced detector.
If the balanced-pair distortion is a small fraction of that, say, 1% or less, then you still get balanced-detector distortion but much reduced in level. If the balanced-pair are 100% distortionless, then current draw is constant, with no variation. But distortionless balanced pairs exist only in fantasy, so there is always some variation in current draw with real circuits.
In a Class AB amplifier, it is worse, with three regimes ... Class A at low levels, and clipped-off Class B at higher levels.
This has an impact on the sonics of the supply. A single-ended amp is simple ... improve the musicality of the supply, since music is directly impressed on it. Push-pull is more difficult ... the modulations on the supply are a mix of residual imbalance and balanced-detector artifacts, and significantly worse if Class AB artifacts appear in the output stage.
This is the strongest argument for stage-to-stage isolation, so distortion artifacts from a high-level stage do not modulate a lower level stage, In the Raven and Blackbird, we go the additional mile by having a shunt regulator for the input section. The shunt regulator operates by having a current draw that is the precise inverse of the audio-circuit fluctuations, so the net current draw is constant.
By contrast, in a generic Dynaco or Mullard circuit, we have several topologies, with only simple RC power-supply filtering between stages. The output stage is typically Class AB semi-pentode, the driver is Class A triode, and the input is single-ended triode. All three have different distortion signatures.