Tim, visited the Valley in between two Stadium rounds last month. My intuition is that the perceived difference in playability between the courses is basically a function of conditioning, at least in January, when the Stadium rough is not getting mown. In a world where both courses are maintained equally, they would be of a similar difficulty level, if for different reasons.
Architecturally, Dye's Valley suffers in comparison to its neighbor because at the Stadium Dye did something rare for Floridian golf in creating an intimate routing and shaping the land to create eighteen unique environments (this may be a slight stretch, but I'm not thinking particularly hard about Stadium here). PGA didn't give him the budget to do that twice, so instead he did the easy Florida thing and built up one side of most of the playing corridors and dug out the other to hold water. Basically solving the Sawgrass-is-a-swamp problem with a bulldozer and gravity. Now honestly there are some pretty good holes in a vacuum, but I got tired of the same visual eventually. It's water down the right (and generally homes down the left) through eleven, then everything flips from twelve in.
It's an interesting case study in how many variations on the theme can be produced, but eventually the same old thing gets old. I've never seen a course this likely to produce a scorecard full of pars and doubles.