Express is counter service, Cafe is table service, and Dining Room is more upscale table service. We went to the Cafe last August and we're going back this year - it was very good and the portions were large.
The Cafe has a wonderful assortment of foods, and you can almost always get in on short notice -- sometimes without an ADR if you go early in the afternoon.
Upstairs is great for a special occasion. It's not quite as noisy as the Cafe -- which can be pretty lively at times -- but it has a fun and festive atmosphere all its own and some terrific upscale cuisine. But it's not stuffy -- you can get by with "theme park casual" wear, and even shorts.