Audyssey uses FIR filters, which are not linear phase. I have reason to suspect a lot of the deleterious effects of Audyssey is that is mucking up the careful time alignments inherent in the design of the speakers. Also the room responses are downgraded by Audyssey.
Dirac I have no experience of, however Dirac uses IIR filters which have a far superior phase response.
Since I have designed all my speakers, I am able to tweak them as desired.
So I do not like Audyssey at all, and suspect many of you, if not all, would be better off without it.
On what you said about IIR and FIR filters, I suggest you research the topic more thoroughly and may be make a correction (that would be nice since you are highly regarded on AH) to avoid readers who may interpret your kind of definitive styled statements incorrectly.
On the topic of FIR vs IIR (obviously the more you search, the more good reads one will find):
FIR vs IIR filtering (minidsp.com)
FIR Filter Properties - dspGuru
on_room_correction.pdf (diracdocs.com) Note: This was written by Dr. Johansson, CEO of Driac Live.
Also, as Wiki summed things up here:
Infinite impulse response - Wikipedia
Advantages and disadvantages
"The main advantage digital IIR filters have over FIR filters is their efficiency in implementation, in order to meet a specification in terms of passband, stopband, ripple, and/or roll-off. Such a set of specifications can be accomplished with a lower order (Q in the above formulae) IIR filter than would be required for an FIR filter meeting the same requirements. If implemented in a signal processor, this implies a correspondingly fewer number of calculations per time step; the computational savings is often of a rather large factor.
On the other hand, FIR filters can be easier to design, for instance, to match a particular frequency response requirement. This is particularly true when the requirement is not one of the usual cases (high-pass, low-pass, notch, etc.) which have been studied and optimized for analog filters. Also FIR filters can be easily made to be linear phase (constant group delay vs frequency)—a property that is not easily met using IIR filters and then only as an approximation (for instance with the Bessel filter). Another issue regarding digital IIR filters is the potential for limit cycle behavior when idle, due to the feedback system in conjunction with quantization."
Whether Audyssey's filters are linear or minim phase, it wouldn't be because it is FIR because it could do either (may be both too I would assume) depending on implementation. As often is the case, there are pros and cons of each, Dirac is smart in claiming the benefits of taking the advantages of both.
I highly recommend those interested in the popular Dirac and Audyssey to read the Audioholics.com interviews in order to get the info directly from Dr. Johhansson (Dirac) and Dr. Kyriakakis (Audyssey founder)
Dirac Room Correction Interview With Mathias Johansson | Audioholics
Audyssey MultEQ Room Correction Interview With Chris Kyriakakis | Audioholics
To quote some of what Dr. Johansson said in interview:
"...Dirac Live uses a proprietary structure that is neither plain FIR nor plain IIR..."
"...Dirac’s solution is to use the best of the FIR filter (mixed-phase correction, i.e. time-domain correction) and IIR’s for what they are best at...."
I have read many articles on the FIR vs IIR topic and from my understanding, again, both have their + and -, but if processing power is not the limiting factor, FIR appeared to be superior overall for REQ applications. Dirac Live's approach to use sort of a hybrid approach does sound convincing and I believe eventually, if not already, they can do a better job than YPAO, AARc, Audyssey. I have read little about Trinnov, but to me if they were the best or not it wouldn't concern me at all because there is no way I would pay the high premium when I am already happy with Audyssey.