I'm not sure how helpful this is as I have not heard an Anthem surround sound processor.
I recently replaced my Marantz AV8801 processor (top of the Marantz line at the time) with the AV7704 (second tier). To my ears, the AV7704 sounds as good as the AV8801 did and it does Atmos, although I don't have any height speakers at this time. My home theater sounds as good or better than most theaters I've been to.
I have heard the Anthem integrated and the room correction in that piece seems to work really well, but it had a "digital" sound to it that made me very aware that it was engaged. It sounded great, but I was always aware of its presence if that makes sense. I don't get that sense with the Marantz Audyssey room correction engaged for home theater, but I don't listen to the Marantz in two channel mode, if I did it would probably be similar. I prefer no room correction for 2 channel listening.
When I was doing my upgrade I spoke with my local dealer and they said the Anthem room correction is better than Marantz, but they carry Anthem and don't carry Marantz, so a grain of salt must be taken.
I have a separate two channel preamp (Modwright LS 100) that I use for two channel listening. I'm a lot more critical of the two channel aspect of my system than I am for home theater.