Just compared D2's HPO and DAC2. DAC2's HPO is really a bad match for HD800. It sounds flat lacking dynamics and stage, and it doesn't push the HD800 to push out details like the Hugo. Normally, HD800 should sound spacious, but with DAC2, it's pretty flat, so I'm puzzled. It's the most harsh sound I've experienced with the HD800 preventing raising the volume up for dynamics if there are any. It's worse than Hugo with the HD800. But, with iems, DAC2 performs better than the D2 and Hugo, it's sounds very accurate and real with iems. D2 sounds dry with iems, but not with HD800. Possibly, it needs to be be dry at a more sensitive level to be detailed with less sensitive headphones like the HD800. I'm noticing a trend of integrated DAC/Amp with high resolution with iems, but not so with HD800(Hugo and DAC2 being in that trend). I'm guessing you can't match both iems and HD800 at the same time with the same amp.
I personally think the D2 is the best integrated DAC/Amp I've heard with the HD800. Possibly, the DAC2 needs an amp that can push out the resolution better than the built in amp.