I eventually bought a Bryston, after auditioning cdps from Arcam, Cambridge, Naim, Primare, and Rega. Unfortunately, I wasn't able to hear the Ayre.
The Arcam FMJ 37 was probably the most analytical of the bunch. It impressed on first auditioning, by really separating out very distinctly everything that was going on in a complex recording, but as one listened on, it became clear that it could be fatiguing over the long haul. Timbrally pretty neutral I would say.
The Rega Saturn struck me as middle of the road, clean, but ultimately a little "polite".
The Primare CD31 and Naim CD5x were both good, very listenable units, relatively warm and well-rounded (good timbral qualities), players that one could no doubt live with long term, but which ultimately didn't distinguish themselves, didn't stand out from the pack.
The Cambridge Audio Azur 840c was my runner up. I went back and forth a couple of times between it and the Bryston. It was neither too analytical nor too warm, very balanced, good timbrally, lots and lots of air. Instruments floating in three-dimensional space.
The BCD-1 has many excellent attributes, but what struck me most (or what struck me first), was its authority in the bass. I'm guessing that this has to do with how Bryston handles the output stages. It is in another league compared to all the other units I've mentioned. It gives the music an incredible robustness. As I listen mainly to large-scale, nineteenth-century, orchestral music, this is a particular plus for me. When the massed double-basses really dig down deep, they really dig. (Think the opening bars of Mahler's 2nd.) This in turn gives the rest of the reproduction an excellent base (no pun intended). Very fine player also in terms of neutrality, timbral rightness, soundstage, imaging, etc. I heard none of the "dryness" I've occasionally seen mentioned in reviews. Perhaps the 840c nosed it out in the "air" department, but after considerable back-and-forth auditioning, the BCD-1 was a clear winner.
I think the Cambridge and the Bryston are excellent units. I'm sure the Ayre is too. Beyond that, it's more a question of system synergy, and what qualities are particularly important to you as a listener. As usual, horses for courses.