Hey Sphinxvc--
Presuming you mean the PS Audio DL III, that is the DAC I used for over two years before getting the Bifrost. My DL III is modded by Cullen Circuits.
Big differences are tonal balance and detail. The PS Audio is more "analog" sounding. Most people understand this to mean warmer, with the top end less emphasized and a bit more mid and low bass. The DL III is exceedingly pleasant to listen to and removes all trace of digital nasties.
The Bifrost is lean and mean (like me, at least the mean part is like me...) and does not add any energy to the bass. That is not to say the Bifrost lacks bass - as I have confirmed on many cuts it does go all the way down. This may lead some to call the Bifrost thin or bright, but that's only in comparison to more colored DACs. The Bifrost is a bit like the genius child who says exactly what's on his mind regardless of the social setting. Illuminating if perhaps ocassionally uncomfortable.
On the cut Coffee Homeground from her Lionheart album, Kate Bush belts out "lipstck smeared" in a high voice, followed immediately by a strong flute note. Reproduced poorly, these events can be excrutiating. The Bifrost delivers all the power of Kate' voice - you get the feeling she's not only putting her whole diaphragm into it but probably standing on her toes as well - without going over the edge. Likewise the flute is enough to make you jump, but in a good way.
The Bifrost is also hyper-detailed. Touches that might usually be lost in the mix are almost floated on their own whether on phones or speakers. On albums that tend to come across like sonic walpaper, this can be a great thing, letting in more space and light. With some recordings, though, the Bifrost almost disassembles the mix, giving a trees-rather-than-forest perspective. Or to put it another way, spotlighting the individual stitches over the whole tapestry. This seems to occur more often over phones.
I also think the Bifrost tends to convey more eneregy, more pace to the music. It's worth keeping in mind that the PSA DL III is an upsampling DAC where Schiit expectorates all over upsampling.
If you prefer beauty over unvarnished truth, you might very well prefer the DL III. If you can't bear to think there might be information you might be missing, the Bifrost gets the nod. Also, the PS Audio is made in the People's Republic of China, while the Schiit is made in the USA (well, the People's Republic of California.)
These days, I'm using the Bifrost more and the DL III less.