I am not sure if this will be any help but I recently did an in house comparison between the AX-7e and the Hegel 160. In my system the AX-7e with the Codex sounded much better with my Harbeth SHL5+ than the Hegel. I also tried using it with my Vandersteen VLR Wood's with the same result. I use an Aurender N100H to feed the Codex and all Audioquest cables. I would suggest you find a dealer and try the Hegel at home, in your system, before you pull the trigger on this.
I found the Hegel to sound clean and clear but not very musical. The Ayre combination sounds more like music to me. YMMV and this is only my opinion. I really wanted to like the Hegel as a one-box solution, but I could never warm up to it. It may be that the Röst has a more musical sound than the H160 so again; I would try it in your system. Good Luck!