For me, even though I have a room that is horrible for acoustics (great room that has family room, dining, and kitchen in one open area), I have never been fond of what EQ does for the sonics in my room. I've had a few processors with Audyssey, a couple with Dirac Live, and one with RoomPerfect. If I had to choose a processor with EQ, it would be RoomPerfect for me since that sounded the best in my room. So, I look for the best sounding 7.1 processor without using EQ. For me, that is the CBIV. I'm sure Dirac Live helps for some folks and makes the CBIV even better for them, but for me, it just doesn't work in my room.
Regarding Trinnov, I've heard it's better than RoomPerfect. However, it's still EQ, so I'd want to hear it in my room to see if it would work for me. Because my 4 surrounds are in the ceiling (no rear wall on my family room), then Atmos, etc is kind of out for me, so 7.1 is the best I can do. In my case, I rely on the great engineering in the Theta DACs and power supply to give me the best sonics for my room.