I own the original FMJ cd-23 (not the text version) and it's been a great-sounding, reliable player. Decodes HDCD, too. (not sure if the newer players still do that). I have never a/b compared it directly to the newer 33 or 36 in my system, however.
I worked in a shop that sold Arcam (and Meridian, among other things) during the late 90's to early 00's and had the chance to get product training from the Arcam factory reps on the features/benefits of the Ring-Dac design when it was first coming to market in their players. It certainly was ahead of it's time in 1999 for a $2k player and I suspect that's why they can still hold their own today and sound great. I spent time in the shop listening to the cd 23 compared to the then-current Meridian 508-24 and bought the Arcam. I just couldn't justify the huge jump in cost for what to me was not a night/day difference in sound. To me the Meridian was a touch dryer-sounding and there was something about the Arcam player that really reeled me in to the music.
The main reason the Arcams no longer use the Ring-Dac is that they only licensed the technology from DCS for a short period of time. I never heard of the difficulty to manufacture/reliability issue as a reason to discontinue it although I suppose that's possible. I suspect cost was probably a bigger factor, though. Also, the Ring-Dac in the Arcam player is not the full-blown spec found in DCS gear, rather Arcam used the major elements of the DCS design to create a custom chipset to be used first in their Alpha 9 and later FMJ series players. It's like getting the low-fat version of the DCS stack, Sounds great, without the guilt! If you are on a budget, you might want to try to find an Alpha 9 which will cost less than an FMJ series player and still have most of the performance.
As for comparing the sound to an Ayre or MF, I can't help you there. But my experience with the FMJ series Arcam is that it's very well made gear and it's fair to say the performance will hold it's own against more expensive equipment from other manufacturers even today. Of course it's all a matter of personal taste when you get to that level of performance anyway. Good luck! JZ