That's a good question, I think the HRT HD is very good, giving you quite a bit more precision over the Music Streamer II standard. The mids could be a bit thick and congested with the MSII, whereas the spacing is much better with the HD, and you get quite a bit better extension in the highs and lows with the HD. I think especially if you already have the Wyrd, it's a good option. Also, I might be crazy, but I think the ASIO filter used with the USB 2.0 software that comes with the HD provides smoother highs, even though there is still a lot of information up there. I don't know if the MSII+ goes up to 192/24 with USB 2.0 via ASIO. If so, it may not be that much of a jump.
DACs are notoriously hard to compare and review because in the best case, many people think, a good DAC gets out of the way and lets the music through with no commentary. HRT seems to feel that warming up the sound a bit is a good idea. This makes some tracks feel hot and bright, unfortunately, but most of the time with good recordings it sounds very smooth and detailed from top to bottom.
With the DT150s the HRT HD seems to be a good match, and I wouldn't personally spend thousands on a DAC today, given how fast the technology is changing. In fact, you may want to wait and see if HRT comes out with a new flagship DAC, since the HD has already been around for about two years. The next DAC will probably include native DSD and claim to have a lower noise floor without needing some kind of external linear power. Perhaps it will even have its own external power supply. In that case, I would probably upgrade, as well.