So I devoted some time to listening to the two and tried to do my best to compare them (my hearing is not the best, but I tried - too many loud concerts as a kid).
To start off, I think they both do an excellent job of recreating music and depending on your budget, you couldn't go wrong with either. There are a few minor things to consider between the two:
1) The Bryston as it stands right now can handle the highest resolution files that you pass to it, up to 192 khz; whereas the Wadia only works with files sampled at up to 96 khz (I am certain that Wadia will eventually develop an upgrade so that it can handle files sampled up to 192 khz)
2) The Wadia (if you get the "U" upgrade), handles USB data better (up to 96 khz) than the Bryston (up to 48 khz) currently does (although I was told by Bryston that as technology improved, this could be upgraded). NOTE: I do not have the USB feature on my Wadia, so no comparison was attempted.
Having said all of that (plus the Bryston just received a Golden Ear award from Absolute Sound for 2009), I hooked up my Wadia directly to my pre-amp and ran a digital coax cable from the Wadia to the Bryston which I hooked up to a separate input to my pre-amp to run the comparison.
I listen to primarily to rock music mixed in with some jazz and country, so different music types may give different results. For this comparison I listened to the following:
Brian Eno - Another Green World (Caroline Records Japanese CD pressing - I believe this was taken from DSD master)
Stevie Ray Vaughan & Double Trouble - In Step
Luna - Penthouse
The Waterboys - A Pagan Place
Lyle Lovett - The Road to Ensenada
I don't really want to bore people with track by track comparisons for songs, but I will say that at the end of the first round of listening I had a difficult time discerning a difference between the two. So I went back and listened again. The second time around I just closed my eyes and tried to imagine how the musicians were set up in the recording to see if spatially I could detect things. Well this was where I was able to start to detect a difference between the two. My ears began to register that the Wadia was a little better at placing different instruments (percussion specifically on a few of the Lyle Lovett songs) into more defined locations than did the Bryston. It also seemed that the instruments came through a little cleaner to my ears and I was able to separate one from another a little easier. Again, this is to my ear and unfortunately not a blind test so there is most likely some bias in my results (as possibly would the selection of the "C" digital decoding algorithm, which was my preference of the three options available on the Wadia).
I really don't think you could go wrong with either. Had I not been given the opportunity to acquire the Wadia at such a ridiculously low price, I would have been extremely happy with the Bryston as my DAC (I had originally purchased a Bryson and Benchmark to do a comparison and I preferred the Bryston hands down to the Benchmark - although really liked the integrated headphone amp of the Benchmark). Now I am left with the decision of keeping both or just keeping the Wadia, not going to be an easy decision.