The “leakage current” is only an indicator of changes, not the reason for change in the sound*. In a common “traditional” power supply (iron core transformer, split secondary winding, rectifier and a pair of reservoir capacitors) the dynamic of what is happening when it is used with an audio amplifier, especially class AB/B, is quite complicated and every component can affect the sound. A possible approximation would be a diode mixer producing a complex interference pattern by mixing the pulsed mains frequency current with a distorted amplified signal current and all that goes through reservoir capacitors (which are not completely linear and nonlinearity changes in time during run-in. The simplest way to observe the difference is to look at the intermodulation products for an amplified multi tonal signal.
Cheers
Alex
* - however it is a useful parameter as the speed of the “leakage current “ changes is a good indicator of how fast a particular capacitor could settle .