Bryston Bda3 vs 3.14 Streamer

Running thru USB with out it.

For an upgrade in sound quality I would just get a separate streamer and keep the BDA-3.
Something like the new Lumin U2 Mini should be nice with a good USB cable (or even AES/EBU). You can use Lumin’s AirPlay to stream from YouTube and either Lumin native app (hideous, probably just as bad as Bryston’s Moose) or Roon for streaming services.
Gives you more flexibility and keeps the potential noise makers out of your DAC  

No.  The streamer sounds good but the program that runs it, Manic Moose, makes it a non starter

What streaming service you got? Manic Moose only supports Tidal and Qobuz but a bunch of internet radio. Any locally stored files or interest in that? Any interest in playing CDs or ripping them to storage.  Any interest in exploring ROON?