It seems like an impossible task to compare Audyssey to Dirac in a useful way, but maybe somebody will come up with a method that's meaninful. I have two systems that are vastly different, with one running Dirac Live on a miniDSP Flex while the other is Audyssey XT32 on a Denon AVR-X4300H. I do happen like both a lot, but I don't know how to compare them in a way that would be meaningful to other people.
miniDSP Flex w/ Dirac Live
Topping PA5 powering Revel M105s
Crown XLS1500 powering two 8" Dayton Ultimax based subs I built
miniDSP handles 24dB/oct LR crossovers at 80 Hz
No additional EQ, Dirac Live is the only correction used
*Treated 115 sq/ft office and used for near field listening at 3 feet
Denon AVR-X4300H w/ Audyssey XT32
Internal amps powering Focal Aria 936's
Two JL Audio e112 Subs, first corrected with MSO filters on an miniDSP 2x4
Denon handles crossovers at 80 Hz
*Untreated 1000 sq/ft room and used in a TV/living room at 11 feet
It is clearly not useful to compare the setups as they are now since everything is vastly different between them, and they are obviously in different rooms. However, I really like both of them for how each corrected for the room it's in. I like Dirac's software UI and process a little better than the new MultEQ-X software, but I got good end results from both. Also, after a lot of testing and tweaking with each, I ended up preferring full range correction on both for different reasons (I have waffled back and forth on this one, but that's where I am now).
I have the time and interest to try and perform a valid comparison, but I'm at a loss for how would one design a valid and meaningful test using a config people would care about.
When I say a valid and meaningful test, I'm mostly meaning setup and configuration stuff. For example... With Audyssey, I was able to get the best sub response across 2 seats by using a miniDSP and Multi-Sub Optimizer first, and then running Audyssey after that. Since Audyssey XT32 only has one sub correction curve that's applied to both subs, getting better results with MSO isn't surprising, and the results were substantially different. However, I was able to get better sub results in my office with Dirac all on it's own and no MSO EQ. I tried it both ways. Since Dirac Live corrects only R/L, and the subs are crossed with the mains at 80 Hz on those channels, it corrects the L main with the L sub and the R main with the R sub. So while not exactly independent sub correction, it does effectively EQ each sub on it's own. When I used MSO the results were odd and I didn't like it, but I also think a lot of that could be the room and near field use case.
I feel like no matter how I set a test up, people would be like "well that's not really valid/useful/interesting/etc because you set up the subs not the way I would use them bla bla bla." And then do we care about how well each one was able to be tweaked to it's best and most optimal curve (adding parametric EQ in the Audyssey software, or making changes in the Dirac curve)? It seems that is more of a test of how good I am personally with dialing in each one, but in the end the ability to tweak those things does make a difference. Would we only care about base/default curves? But is that valid if most people want to tweak it for different results? Adding in MSO throws in a ton of variables, but Audyssey sucks at more than one sub, and Dirac Live thinks sub's are just the low end of your R/L channels, so I don't even know where to start there.
In other words, I think due to the level of complication and the number of options involved in the setup/config of each system, I can't see how I could actually do a valid and meaningful test for anybody other than myself. I'd say the same of other people as well, but maybe somebody has different physical gear that makes this easier to test in a more broad way for others.