The HP section of the D1 Dual is really good. With my LCD3-F I had hard to find a difference to my Master 9, maybe the Master 9 had little wider soundstage and was a tad more transparent, and the SE out of the Dual sounded a little cleaner - but I was not sure.
The D1 can even handle my HD800 well, but with the Sennheisers I prefer the Master 9 which helps the HD800 to come to life. The gap should be closer if you use the balanced outputs of the D1 with adapters. It is really worth to give the D1 a try before you buy a headphone amp.
Bmichels found that the SE out of the Dual with the HD800 sounded better than a Cavalli Liquid Gold! Maybe the Master 9 is better than the Liquid Gold