When you compare amplifiers by loudness, the voltage value, expressed in dBV, should be used. The difference in voltage will show the difference in decibel (dB) between the amplifiers.
The power values in regular mW do not convenient to direct comparison.
The direct comparison by power is only suitable for speaker amplifiers operating with an ultra-low-ohm load. This does not apply to headphone amplifiers where the headphone resistance is higher than 8-16 ohms.
Because of the higher resistance of the headphones, when compare the volume of a musical signal it is necessary to simultaneously take into account the current and voltage limits. The speaker amplifier have limit by current. For the exact difference between the amplifiers in decibel, the power value must be converted into voltage in units of dBV, taking into account the margin by current for the music signal to 12 dB.
If made a comparison simply by power, then the error will reach up to 12 dB. When sorting by volume
, you can see that at the same volume values in dBV, the power values in mW will be different.