I think this answer depends heavily on how your family plans to eat. DDE is primarily usable at table service (TS) restaurants, while
DDP includes a mixture of table/counter service meals. One other thing to remember, is that AP holders get a 10% discount at some of the TS restaurants (particularly in EPCOT).
There are exceptions to the TS rule. In AK, DDE offers you discounts at most of their CS restaurants, since they really don't have TS there (just rain forest cafe). That's a great use of the DDE! I LOVE Tusker House!
Also, all of the values (and maybe some of the mod) food courts take DDE. In fact, they even give you the 20% of the refillable mugs (wish I had known that in March!).
Giving you an idea how it might go, I'll sum up our March spring break trip food-wise.
We made one PS for each day (almost always shared meals at a late lunch because we're small eaters), ate breakfast in our room, had 1-2 snacks a day, then a light shared CS meal at night.
Before the trip, I wasn't planning on the DDE, but when I ran out my expected expenses, I realized that the DDE discount would pay for itself that trip, and since we're so close, we'd use it a lot. The final kicker for me was the possibility of my parking fee being returned if we used the DDE within 3 hours of entering a park (Fl seasonal pass holders pay for parking). So I ordered it and picked up the temporary card the morning we got there.
By the end of the trip, we had saved around $80-$90 using the DDE. So it was worth the money for us. Since that time, I have exclusively used DDE at food courts and beaches and cream. Probably about $25-$30 savings total.
The only time we will do the DDP is this September, during
free dining. And even there, I plan on spending almost nothing out of pocket since we'll still share TS and CS meals to cover breakfasts as well.
One final thing to remember is that I think DDP requires you to buy a base ticket in order to qualify for the package. So you have to factor that cost into your budget assessment.
Good luck!