Hated the HRT MSII for the HD-650. It's nice if you want the HD-650 even warmer and with even less treble and more forward sounding upper mids. I'll pass! The ODAC made every headphone I have even smoother sounding than with the MSII. Weird. Soundstage on the MSII is also not good IMO.
Odd. My experience is pretty different from yours. An ex-coworker of mine (who is also a head-fier) came by and we compared gear, including my MSII versus his ODAC. We used both the HD650 and the HE-500 and had the O2, Bottlehead Crack+Speedball and Burson Soloist amps as options. In the end, we decided that the two were very hard to distinguish. He was questioning if there was a difference... I felt that the MSII had a very very slight improvement in soundstage and musicality, but so slight that it wouldn't generally be noticeable. Basically, we felt them on par with each other.
Also, I should mention just for the sake of the guy who originally asked the question, I heard there is a big difference between the HRT Music Streamer II and the Music Streamer II+, and I'm seeing that in their prices on Amazon, too (~$150 to ~$350). Not saying I don't believe in your review of the MS II, but I just wanted to let the guy there's a difference between the two.
At the recent SF Bay Area meetup, someone was selling their MSII+ for a reasonable price and I did a quick A/B versus the MSII with my gear and easily noticed a difference, so I bought it on the spot. When I got home, I did some more comparisons. While the general presentation is similar, the plus unit makes big improvements on soundstage, clarity and detail. Brought it to work to let a couple of guys who recently bought Schiit Modis to compare, one who has a great-sounding old STAX setup on his desk (that he lucked out and got a great deal on ebay) and was wondering if this whole DAC thing was snake oil. He's not wondering anymore.