I agree that I think the CD23 would be a better purchase for the price than the CD33. The 23 used the Wolfson ring dac technology. Then Arcam changed them out for the 33. And now the 36 is coming out. You can get the 23 for about $500 less than the 33, and the jury seems pretty split between which is better. And I agree with Bigtee's assessment, the 23 just has a very smooth, pleasing sound.
However, at least for me, the Ayre is superior. Primarily in the bass, fuller and deeper. With a wider and deeper soundstage where there is more space between each instrument. I agree also that the Ayre transport takes longer to load up than the Arcam. When I heard 1 upgraded to the e version, the transport became dead quiet. Before you could here the disc spinning when you listened at low volumes. And the bass and overrall dynamics improved. To me it was worth the $400 upgrade, but I think it's pretty special before it as well.
You really can't go wrong with any of these 3 players IMO. The biggest advantage I heard from the Ayre was when it was ran balanced instead of single-ended. If you currently run balanced or are planning to, that's the route I'd go. If single-ended, get the CD23 for $1100 or so and don't think twice about it. Good luck.