A local place defines these three styles that they offer as follows:
New York Thin Crust
Thin, but not razor thin, ask for extra thin if you like your pizza real thin.
Chicago Deep Dish
Thick & bready, with a big lip to hold everything in. A little cornmeal in the dough makes for a hearty crust.
Detroit Deep Dish
Thick & bready, NO LIP. Cheese all the way to the edge of the pan so the crust caramelizes.
Of the three I prefer the Detroit style at this particular joint.
I enjoy all types, but if I could only choose one pizza, it would be a margherita style on a cracker thin crust. If you're ever in Iowa though, get a pizza from a convenience store called Casey's, they are everywhere. It's simple, not fancy; made from scratch and just simply good. It exemplifies what it means to be an Iowan really.