Of course we still can't be certain without that blind test(!), but I think we can say it's not the bits for your particular issue.
If there's no firmware update or settings change for the Lindemann (and I can't see one) then you need to try to deal with any other potential causes.
Do you have the Bryston connected wiith RCA or XLR? If RCA, then plug the LIndemann in using the Bryston's input connection at the amp and with the Bryston's leads and listen, just in case something is up downstream. If you use the Bryston with XLR, plug in instead with what you are using with the Lindemann and see if the sound deteriorates. These are really just a sanity check before you replace the Lindemann (assuming you want to fix the poorer sound). The nominal/specified RCA output of each is 2V, and I don't think we are looking at an impedence mismatch.
We'll define the issue neutrally - your hearing doesn't trust the Lindemann, whether this is something in your head or a technical deficiency. Either way, if you want to "fix the problem" I'd go with replacement, unless you can do the blind test and that restores trust.
When you replace, consider a good DAC and separate streamer, just because there are fewer decent all in one devices out there. You need to be able to test at home and return the replacement if it's no better for you. Don't buy ultra expensive stuff unless it has features you need, or better ergonomics: don't buy magic cables, supports or anything else somebody says will "improve the sound". Just cut out the bad bit. Since you like the Bryston, it's likely you need a DAC that "measures well" - most people will prefer such a DAC. Even so, that's most of them, not just the "best SINAD" stuff.
If you are happy to live with the current sound difference, that's fine as well. Good enough is good enough. But I'm betting that you're an audiophile...