The big differences among any of these AVR are the different Room EQ, sub EQ, and Dynamic EQ (DEQ).
Dolby Volume Modeler is supposed to be the equivalent of Audyssey DEQ. I have not compared Dolby VM vs Audyssey DEQ.
Anthem, Harman Kardon 3600 ($700 on Amazon), and the Onkyo 5007 ($2500) have Dolby Volume.
Yamaha & Pioneer have their own versions.
Denon & Marantz have Audyssey DEQ.
IMO, if you do not use subwoofers and just use full-range towers, Anthem is the better route because it will allow you to EQ just the bass of your towers.
If you use subs and don't care to utilize the bass in your speakers (XO 80-100Hz), I think Audyssey is the better route because it can bypass the front L/R EQ and just EQ the subs (DEQ). That's what I am thinking.
You can always try the Anthem and compare for yourself. Return the Anthem if you don't like.