Well, I am solidly in the Audyssey camp - I have Audyssey Pro that I use with my Denon. I am sure you will get mixed replies, but my opinion is that Audyssey probably has more R&D behind it.
I did own an Pioneer Elite AVR many years ago. I made the "mistake" of buying the service manual for it, which also was for the non-Elite version. I had thought that the Elite might have better "parts" but almost all had the same part number. The only exceptions were a couple of features that the Elite AVR added. Again, this was back in the Laserdisc timeframe, so things may have changed a lot since then. But at the time I asked myself why I spent the extra $s, other than the Elite version had pretty simulated wood end panels.
I did own an Pioneer Elite AVR many years ago. I made the "mistake" of buying the service manual for it, which also was for the non-Elite version. I had thought that the Elite might have better "parts" but almost all had the same part number. The only exceptions were a couple of features that the Elite AVR added. Again, this was back in the Laserdisc timeframe, so things may have changed a lot since then. But at the time I asked myself why I spent the extra $s, other than the Elite version had pretty simulated wood end panels.