I'm sorry, I was away (vacation, then was very busy on work), so if somebody still interested here is my report.
First thind I did, I purchased D2... and returned it after couple of days....unfortunately this thing simply didn't work. Looks to me as pre pre BETA release - half of the functions doesn't work, crashing all the time, files doesn't show up, ....very long list of issues. Firmware updates doesn't help... never mind. I've returned it - it's not an option.
....But I've purchased K701 as well, and I connected it to the headphone output of my MacBook ( known to be quite good sound quality wise ) with no amplifier, and.... yes, I was blown away by it's sound. This thing can really fool me that I'm listening to the REAL sound, even without amp.
Sometimes (on some good record) I completely forget that I have device on my head - this is quite important point - NO OTHER, cheaper, but more suitable for mobile use alternatives, like Sen. HD555, 595, DT770, etc. (that were recommended by many here on this thread, as more adequate alternative to K701 without amp) CAN NOT DO IT for me! My brain simply can't, believe to their sound. I always feel some artificial sound source on my head. K701 is more like $3000 speaker system.
So, if it sounds good out of MacBook, it will DEFINITELY sound at least the same out of D2, since it suppose to have much more powerful amp inside
...well, of cause, bass is, let's say it politely, "very special", in fact - almost non existent. It was expected. I don't know is it a an absence of amplification, no burn-in, or just it's their nature.... yes it little bit thin, not full enough (but still OK), so I'm going to get an DAC AMP combo anyway - ZERO 24BIT, or EMU 0404 usb (not sure it has enough power for k701???) sounds very promising.
As for semi portable use (at home) the only alternative I can see is a decent DAP ( Trekstor vibez, may be Kenwood $$$ ) and some portable amp... or to get another try with D2. This player seems to be very sensitive to files it plays. Some files it plays, some not. May be it is possible to make it work, it just a matter of time, which I don't have.
Summary: I extremely satisfied with K701 as it is, but of cause I realize that it's not the final performance, there is a space for improvement, and I can see it clearly now. Special thanks to JaZZ and Gurra1980 who convinced me to get it!
In a meantime several people strongly recommended me to try etymotic ER4P, claiming, that they will sound at least on pair with K701, but in portable variant. Today, I finally got it from e-bay, so I will be able to compare these two. I'll post the results soon. Could be interesting comparison. It worth another thread.