Higher or lower impedance has absolutely nothing to do with the power required, nor does the quality of the headphones.
Headphones with either low or high impedance can have high or low sensitivity; the power needed to achieve a specific volume level depends on that sensitivity.
That is precisely why I explicitly stated that there is no difference provided there is sufficient power.
A balanced headphone amplifier uses two output stages per channel—compared to the single-ended output's one—in a push-pull configuration. Theoretically, this yields four times the power, a figure the K7 comes very close to achieving.
The downside is increased noise, resulting from the noise of both output stages being additive.
That is really all there is to it. If you drive a pair of headphones at the same power level using either output, there is no difference. If that isn't possible, it simply means the single-ended output lacks sufficient power.
Unused headroom does not result in any change to the sound.