No, with Audyssey or MCACC, you don't need an external EQ.
I think Denon and Onkyo are delivering really good value nowadays. I'm predisposed to the Audyssey system rather than something proprietary, though. YMMV. Shop for features and price.
I think you'll be really happy with the Axiom setup you've chosen.
Some years ago, I had the chance to hear - back-to-back, in the same room - an EP600 and PB13-ultra. Obviously, those are not the current models you're looking at, but it was a very interesting experience. I have an older SVS PB12-ISD. I think SVS subs are terrific.
AND there was a definite signature sound to the SVS. To me, it was heavier and fatter. Though the test was blind, all four of us could easily identify each sub. The Axiom was drier and more nuanced. I preferred the EP600 and that's what the forum member elected to keep after extended auditions of both in his home. Both were stunning.
I believe that Axiom sub design philosophy places a higher priority on lower distortion than some other manufacturers. There is a general belief that - at very low frequencies - distortion is less audible and/or less objectionable. I'm less sure.
How big is your room? How many people are watching movies with you? Listening to music with you?
You might start with an EP500 and see how that goes. Axiom will let you upgrade during the trial period for free. If the EP500 doesn't go low enough, you can get an EP600 or EP800. If it doesn't cover enough area in your home, you can get a second one. It's pretty hard to model/predict how your ROOM will interact with the rest of your system.