I've only just started using Dungeon Tiles, having used a drywipe grid mat for a long time. I'm actually quite impressed with the quality (and the quantity) of dungeon tiles. I only bought two packs, but already I have more dungeon scenery than I could ever use. I'm now looking for some wilderness/outdoor packs so I can use more varied environments.
It is probably true that it could slow your game down extensively if you are forced to fish in a box of all of your tiles for specific pieces of an encounter area. I have plastic document wallets for each encounter with the tiles I need to use slotted into them along with a brief drawing of the encounter area, ready for quick deployment. I've also experimented with "Encounter Cards" - a write-up of the Monsters, Loot and more interesting elements of scenery - which, if you have the time to prep, basically means you can have "encounter packs" ready to go on the fly.
It is also very true that the Shackled City Adventure Path has some really awkwardly shaped areas, plus some truly whopping ones, for which dungeon tiles probably wouldn't be appropriate. Then again, for the truly whopping ones I suspect you'll find that you can't get a battle mat big enough.
I quite like the tiles, and I think solutions to them slipping around are easy enough to implement to make them pretty damn useful.