Finally I got my HD660S2 delivered. I tried them first at my workplace with xDSD Gryphon (4.4mm balanced) and compared them to my HD660S. S2 was better but I still felt a bit disappointed. There was increase in treble presence and mid bass but especially sub bass quality was not there.
Later today I tried HD660S, HD660S2 and HD800S with my HDV820. Just Wow! I was not expecting how good these S2 sound and how much they scale. And the sub bass... it is there and sounds really good. No need to EQ with these. Too early to make any comparison but I have a feeling that these are not going anywhere in many many years. I will give 660S to my son.
This was an interesting review of the HDV820. It pretty much is in line with my experience when pairing with some of my headphones including HD660 S2.