Only compared the MKI (mine) and MKII briefly so please take it with a grain of salt.
The MKII sounds less grainy than the MKI. On a few pieces this graininess could be interpreted as better texturing, which, however, I'm not really sure about. In general, the MKII has a more natural sound and is less fatiguing than the MKI. From the time I spent I couldn't tell whether the MKII had superior detailing.
The soundstage was better if I remember correctly. Again, not enough listening to form a proper judgement and further, volume matching had to be done manually because the MKI and MKII had different gains. Anyway, despite all these excuses for a straight answer, the difference was there. Better coherency, naturalness and a feeling of improved effortlessness would be the main aspects I noticed.
You could also ask JaZZ about it because he did the same comparison and has better-trained ears.
In any case, I think the main improvements from the MKI is that the MKII has a pre-out. But just ask Jan himself because there are too few people who have heard the MKI and MKII side by side. However, please be advised that Jan is always very humble about the differences/improvements between his amps. When I asked him about a Prehead MKI / HA-2 MKI comparison, he used to tell me that unless I need the preamp capabilities, the HA-2 is just as good as the Prehead. Well, there are a few members on this board who will tell you that the Prehead does sound better than the HA-2 and I doubt that Jan simply didn't hear the differences.