The point is that between low gain (0dB) and medium gain (+9dB) the background noise of the amp does not increase +9dB but will be much less.
Noise in the recording will be amplified 9dB (about twice as loud) though.
On low gain the HD558 will play 5dB louder than the HD6XX.
When you set the gain to M the HD6XX will play 4dB louder than the HD558 at low gain.
You will also increase the noise of the recording by 4dB which is what you may be hearing.
Oh, I see. Yeah, I am not great at the EE/math side of this, so I assume all of that is correct. It's also possible that whatever I'm hearing and labeling as "noise" is really something else (recording noise or something else altogether).
All can say is that to my ears the HD6xxs never sounded as "clean" through the A30 as they do through the RME (or for that matter an old Dragonfly 1.2 I have around) whereas I enjoyed the 558s on the Dragonfly and the A30. [as an aside the 558s sound good through my digital piano but the 6xxs are dull and muffled but again I assume that's because the headphone amp in the piano isn't very good] I fully admit that what I'm hearing and what I'm calling it could be mismatched. I always assumed that the difference was attributed to the Ohm difference. But whatever I was hearing was immediate from the moment I opened the box of the HD6xx and plugged them into the A30 and every time thereafter.
None of this is to be construed as a knock on the A30, it's a fine little box, but in my system to my set of 6xxs to my ears I was underwhelmed with the pairing.