I haven't tried it with those AKGs but when I tried it with my HD600s, the HDP seemed to sound a lot like my Zen music player - bassy enough to psychologically gloss over midrange detail (if you really listen it's all there though), but less bloat. Kick it up over 12 on the dial though (and trust me many people think I don't listen loud enough given they can't hear what I'm listening to at meets) and instead of bloat I hear bass distortion. For some reason however most people seem to have the opposite of my findings.
It's supposedly a great DAC (derived from their most expensive CDP) with an amp and preamp, but when I listened to it, the amp through the analog input was very transparent*, and using the DAC and preamp together into a Plinius power amp and some Polk RTi towers, it was a lot like the sound driving my HD600s, except the upper bass distortion wasn't there.
So the amp being transparent and yet distorts easier with the HD600, off the top of my head there are two possible explanations:
1) The DAC's response might be too coloured and the amp (or at least with the stock PSU) doesn't have enough juice for it, or
2) That PSU - which looks like came off a netbook - might be audibly inadequate**; I'm not sure anymore but check the input V and mA specs on the HDP and the PSU, if I remember correctly the HDP requires a bit more than what that PSU is giving it
If it IS the PSU, and the feedback on the upgraded PSU's gains over it are to be believed, then to some it might be necessary for enjoying it, at which point its real price point for comparison with other products is a lot higher than $400.
*using some Denon CDP at the store, it was noticeable that the sound was different, at least in signature - a bit sweet in the midrange, not much impact on the bass
**also explains contradictory findings, if my theory on crap electrical grids in my country may be presumed, since a bad PSU won't be able to filter all that out and the shop I was in wasn't a believer in line conditioners (which is why, or because, they don't sell any?)