I think it's just a matter of what different people value in a film. You've consistently demonstrated that production values and visual effects are the primary means by which you judge a film. In that case, Batman and Robin would be a natural choice over The Dark Knight, because it was visually showier. I think the people that prefer The Dark Knight value storytelling, subtext and a restrained but well-defined visual style. I think it's unfair to the film to tie its popularity to the Heath Ledger situation, although I agree that his untimely death has caused people to view his body of work through rose-colored glasses.
Regarding this whole Batman thing... I believe that it all depends on whether one reads the Batman comics or has a sort of outsider's view of Batman.
After Miller's "The Dark Knight Returns" and the various reboots/reincarnations of the Batman universe, its characters, its overall tone and aesthetic, all those changes precipitated in the 80's and 90's (think "Knight Falls" and Elseworld series, etc. etc.) Batman became something altogether different from what he was in the 50's, 60's, and 70's... the essential antisocial vigilantism, the essence of a lone man struggling against the world was obviously maintained, but its presentation was completely different. It became darker and much more brooding... Batman's struggles with Superman or even Judge Dredd are alien to people raised on Adam West...
I think the Animated Series was an excellent bridge for both aesthetics...
Thus, it would seem to me that people who prefer the Schumacher films aren't avid readers of comics from the mid-eighties forward... they see Batman more as what he was in early comics and the old Adam West TV series... KAPOW! BAM! <crazy jazz trumpets sound> A Joker who's more mischievously evil than psychotically evil...
Generally, I've found almost all serious readers of Batman comics from the last two decades or so are heavily in favor of the Nolan and Burton films... non-current fan(atic)s prefer the shtick of Schumacher.