Tried to extract any useful technical information out of the 6moons article.

More and more people love the AMP-11R as headphone amp. We thus wanted a more affordable model superior even to the 11R for this specific purpose. With an output impedance close to 2.5MΩ, expect up to 1/10th the headphone distortion with the HPA-21's current-mode output. We believe this will be a true game changer. It's a larger one-box solution with internal battery power supply derived from our EQA-11R."

"As the HPA-21 drives headphones with current, impedance doesn't factor into the equation. We can expect far lower distortion. Such has been studied by Dr. Yoshiaki Muda of the Department of Electrical Technology at the Nara University of Education in his 1996 paper Transient and frequency response of the moving-coil loudspeaker current-drive and voltage-drive method*. During his experiment he found that when a speaker was driven from a current source, he could achieve up to 1/10th its distortion. The HPA21's current output achieves the exact same behavior. The major drawback of current drive for loudspeakers is that whilst there are continuous impedance changes across all audio frequencies, the current-driving force remains fixed. Therefore the unit’s impedance curve becomes the frequency response of the driver. Because of this it is not appropriate to use current drive for most loudspeakers whose impedance varies too greatly.

   "Damping factor with a headphone amplifier is of less significance especially in current-drive mode. The formula for calculating damping factor is D=R/Z (damping factor = resistance of headphone/amp's output impedance). Since the HPA-21’s voltage output is about 1Ω, a 10Ω headphone encounters a damping factor of 10 whilst a 100Ω headphone sees 100. As we see the damping factor varied by a factor of 10. The HPA21’s current output is about 2.5MΩ. This renders damping factor effectively zero. Now the music signal itself becomes the drive current and it is unaffected by any other variables to generate much higher and more precise output drive."

If someone wants to give a shot translating the relevant parts of this white paper which was mentioned somewhere in there, please do: http://near.nara-edu.ac.jp/bitstream/10105/1560/1/NUE45_2_11-18.pdf
Although I think I have a good idea of what it's getting at.

Anyway, I still have no idea how this device is built so that it can support both "modes", and then how one of these modes can measure so much differently. If I had to speculate, I would guess that one of these modes places the load in a feedback loop. Or there's some other feedback trickery going on here.

Anax,

do your conclusions about other HPs not benefiting include the HD 800 as well?

Thanks

Sadly yes.  Others might like the more compressed and slightly bassier output that sacrifices all the HD800's technical strengths, But I think they should just buy another headphone if they like that sound better. 

I tested with HD800, HD600, Oppo PM2, HE5, UERM, ES5, CKM500.  I was originally hoping it would be an option as an uber amp for portable IEMs.  Sadly, it was just the opposite.

That was precisely why I asked the question. I read this exact sentiment (about the bass kicking harder) being expressed and was not sure about how the others (mid and treble) were preserved. Thanks again.

I thought the HD600 in current mode offered the least amount of trade-off and actually recommend that pairing for sure.  It's pretty cool for HD600 owners that want to travel trans/portably.

Here is some reading material:

http://www.current-drive.info/9

For HP amps the 'Grounded Load Operation' part will be aplicable.
Also relatively easy to 'switch' between feedback operations using this topology.
The 'extra opamp' in the feedback loop is most likely responsible for the added background noise of the high Z headphones as it needs to amplify the 'correction signal' more than for low Z headphones.

AFAIK most headphones are designed to be voltage driven (those that perform optimally on low output R amps).
Of course headphones with a flat impedance (orthos and some dynamics) won't react as much as those with wonky or largely varying impedances.
Some may prefer current driven over voltage driven systems as bass and upper treble is boosted.
Headphones that sound 'better' from higher output R amplifiers will probably sound 'better' on current drive amps.

Theoretically (speed related) current driven speakers/drivers will be faster (in rise/fall time) as the current drop caused by the rising impedance of a voicecoil will be compensated.
Unfortunately all resonances that show up in the impedance plot will also be exaggerated.
A blessing for some headphones/speakers perhaps but a nightmare for others.

For orthos though, where the current drive is probably just as good as voltage drive, there should not be that much difference except with this particular design as it clearly has lower distortion in current mode, FR wise nothing will change.