My probably unpopular opinion, is that neither will sound better than the other. Your room makes the most difference in sound, which is why things never sound the same in the demo room as they do in your own home, and speakers make a difference in sound as well. All well designed amps should sound pretty much the same. I wouldn't fall into the trap that states that brand X sounds better than brand Y. The room correction software however can have an effect on what you hear, and ARC is probably better than Audyssey overall, but I'm sure some prefer one over the other. I do have experience with ARC but none with Audyssey so I can't really comment on how they compare.
I have an Anthem receiver in one system and an Anthem amplifier in another system, and at one time had an Anthem AVM20v2 processor and have really liked all of them, so I wouldn't hesitate to recommend them. They are solid, well built units, that do hold value fairly well. Even Anthem's newest designs are a little spartan and perhaps getting a bit long in the tooth compared to companies like Denon who come out with new models every year. When I wanted to upgrade to Atmos, I didn't want to spend the money Anthem wanted on a Atmos capable receiver or processor, so I went with Onkyo and haven't been disappointed. I think you will be well served by either the Denon or Anthem to be honest. I'm not sure what pricing you're looking at, but I'm sure you can find the Denon (or a similar 4400 or 4500) much cheaper than the Anthem, but the Anthem will recoup you a larger portion of your investment when you go to re-sell.
7.4.4 Theater Room: JVC-RS500, Silver Ticket AT 2.35:1 142”, Onkyo RZ830, Anthem PVA-7, Panasonic UB420, Apple TV 4K, JBL Studio 530’s, 4 - 15" DIY Sealed Subs
3.1 Living Room: Samsung 64” F8500 Plasma, Anthem MRX 300, Dynaudio Audience 52’s, Dynaudio Audience 122C, NHT SubOne, Roku Express (2019)