DDE is good primarily at TS (a few CS). It also has dates (holidays) when it isn't accepted. The savings is based on where and how much you eat.
DDP is one TS credit, one CS credit, and one snack credit per person per night of your stay for the money.
If you have both, you can use the DDE at any participating restaurant for any items that aren't covered on the DDP (like alcoholic beverages, smoothies, etc.) Yes, I know that in some places smoothies and milkshakes are on the DDP, but not at most.