For HD 569, interestingly, they sound quieter than HD 6XX on one of my old USB sound card (same volume setting) which I suspect have high output impedance

This is only partially true: if the output impedance of your device is high, you may find low-impedance headphones harder to drive (since it cannot get enough voltage from the output source, roughly speaking impedance splits voltage).For example, when comparing my HD 6XX to these HD 599, HD 6XX has slightly lower volume on some devices, but they sound about the same on some other devices (with identical volume settings)

I will repeat: low impedance headphones are sensitive to source (the 3.5mm jack)’s output impedance

That is the other side of coin that is often overlooked: that high impedance headphones work better with high impedance source, the rule of the thumb (according the blog of NwAvGuy, google it), the output impedance should be less than 1/8 of your headphone to not

This is a minor issue b/c the included 3.mm cable isn't too long to be tucked away and is thin and light to begin with.