Well, you are like most folks, in that you just say Audyssey without any reference to any particular tech. The Marantz uses the MultEQ XT, among other techs. There are more than double digit techs that Audyssey makes.
The variations of MultEQ are the most value rich feature offered in affordable receivers, IMO. If you want comparable technologies from a different company, I dare you to price out an ARC1 capable unit, or even find one with Trinnov (and does it even work properly).
The above said, no one in their right mind would ever say that MultEQ (XT, Pro, etc), is ever any kind of substitute for good speakers, proper speaker positioning, proper listening positioning, proper treating of the acoustical space, proper room orientation, or even proper furniture placement.
Even the touted subwoofer company SVS chose MultEQ tech for their ASEQ1. Of course you then have Marantz, Denon, Onkyo, Integra, NAD, and more. Paul Barton of PSB created a unique target curve just for NAD's Audyssey implementation. Well, JBL now has the BassQ, but that's about double the price of the ASEQ1 or Audyssey SubEQ.
I think what throws most neophytes off besides unfamiliarity is the implementation by receiver companies. Neophytes mistake various implementations to be the fault of Audyssey, and it happens every single day it appears to me.
I think the number one reason that many might not like Audyssey, is because they have become used to overbloated bass. However, if you have any EQ devices, you can always piggyback on top of what Audyssey does for personal preference. There are also multiple target curves depending on the Audyssey capable unit. Many simply say, oh I don't like it, but I am positive that in many cases they don't even know if they are listening to the reference, audyssey/house, fronts, etc curves. They will all sound different. There are also misunderstandings on what delay measurements are, that the various levels set are relative and not absolute, and who knows how diligently they executed the mic measuring process to begin with, let alone even using all of the available measurement points to begin with. List goes on.