I've played a lot more of the top modern courses than I have the classics to this point. Of the 15 or classics I have seen I think most are just excellent courses.
In browsing through some of my photos from the last couple years I came across a situation that does seem to play here, however. Old Corkscrew and The Concession are two recent Nicklaus designs in Florida that I played a little over a year ago on the same trip. In my opinion they are very similar courses--both are extremely difficult especially around the greens with quite a bit of water in play. They both have a few really good holes but neither would rise to the level of TPC Sawgrass, Calusa Pines, or WW Pine Barrens in Florida. Both are very well maintained, although The Concession is quite remarkable in that regard. The aesthetics are very similar, but The Concession is private and Old Corkscrew is a CCFAD that does offer some memberships if I remember right. The Concession has been ranked highly in all of the major pubs including making a couple top 100 lists, but Old Corkscrew barely has merited mention. At least in that case, I have to wonder what has caused the dramatic difference in rankings.
I also wonder if Black Mesa would be much more highly considered if it were private and/or located somewhere other than Espanola, New Mexico. Ditto some of the other great value public courses that don't always make the major lists.