The whole grain buns really aren't bad, but - and this is a biiiig BUT for an operation the size of Disney World - they don't stay soft, moist, and fresh-tasting as long as white buns. I use whole grain buns at home, but I buy them the day we're going to use them or a day before. They don't keep any longer than that before they start getting crumbling and overly dry.
I think when Disney first made the switch they failed to account for the shorter shelf-life and were serving a lot of buns that were well within the "freshness" window for white breads but had been around just a little too long for whole grain. It seems like they've managed to adjust, though. On our Jan '08 trip we only had one CS burger meal (Pecos Bills) and the buns were horrible, but on our Dec '09 trip the buns were still whole grain but fresh enough to actually taste good and stay in one piece.