That's a hard one because there is hardly anything in it but from what I hear from guys that have heard both (I have heard the Ayon - but not the AMR - but I do know people who have heard both) I would give the edge to the AMR.
Note with the AMR though if anything goes wrong its built on one PC board and you have to replace the whole thing. This happened to the guy out near where I live that has the AMR and he was spewing. Also a factor to consider with it being so close the Ayon. And its not a rare occurrence either - I know two that have broken down.
Personally though I would get the new Chord QuteHD which IMHO is as good, or even better than that stuff and pocket the difference - but that just a personal view. I lent my Chord to the tech that fixed the AMR who is building me a battery supply, he is friendly with the owner of the AMR as well, and knows it very well - he thinks it has the edge on the AMR and that's without an upgraded power supply or fed via an Off-Ramp - better bass (in fact I have heard nothing with the bass of the Chord - its amazing), more articulate and detailed mid-range. Before penning this I rang him up just to be sure and he confirmed. This guy knows what he is talking about BTW - he designs and builds the PDX DAC which is also an up there DAC - the Chord is very tough competition.
Thanks
Bill