All things being equal, I prefer DDE because it is more flexible. Want to pop into California Grill for drinks and appetizers? No problem. Want to eat fewer (or more) table service meals than one per day? No problem. Prefer appetizer to dessert with your meal? No problem. Don't want either? No problem. A simple 20% off of whatever you order, wherever you order it (provided the restaurant participates).
The only downside to DDE is that, for most people, the "effective discount" rate is more like 10-15%, after you subtract the cost of the card. But, if you have a family, or take a couple three trips in a 13-month period, it will pay off pretty quickly.