How much you save, all depends on what your family likes to eat, and if you can make the most of the dining plan. My sister is a bit of a fussy eater, so finding restaurants is difficult in the first place. Then, most often, it's hard to find anything on the menu, and when we do, it's the lowest priced meal. We also prefer buffet breakfasts over large dinner, which also means we don't get the most out of it.
I had worked out for us, that if we had to pay for the plan OOP (we're DVC and don't get free dining), we would lose money. For us, it is cheaper to buy our own meals, as and when. However, if you can get it for free, then go for it!!!
Based on the full plan (1xTS, 1xCS, 1XS per day), you can save about $30-$35 per adult, per day. Of course, it all depends on the type of meals and food that you go for. The above figure is roughly what we saved last year, but we did a lot of table service buffet breakfasts, which are some of cheapest table services meal around. We didn't normally go for much more than Hot Dog/Burger/Fries at counter services either, so they were the cheapest too.
If you decided to visit the most expensive restaurants (not including the 2TS credit ones), and bought the most expensive meals that you could get with
DDP, and then did the same with the counter services and snacks, you could be up to the $40 per adult per day saving, if not more.
The only drawback with the full plan is that it is a lot of food, and more times than not, you will leave Disney with a few unused credits, be they table, counter or snack. Our first year on the DDP, when things were a little more relaxed, we came away with just 1CS credit each. Last year, when things were tightened up, we came away with 1TS, 3CS and 5S each! We used to use our snacks to buy cookies as pressies, but they year they clamped down on that and withdrew a lot of the old snacks from the list of those available on the plan.
If you opt for Pop, you will get no dining plan at all. POR will now only offer the Quick Service dining plan, which is 2xCS and 1xS pppd. Check out SSR or OKW, like Wayne said, as they will offer the full dining plan - 1xTS, 1xCS, 1xS