This has always been my take on the DDP:
The cost of the DDP is $51.54, including tax. Most table-service meals for myself (Drink, dessert or appetizer, and entree) total to be about $50 including tax ($35 entree, $3 soda, $7 dessert, $3 tax = $48). Some meals cost more, some cost less. To me, i've found the average to be about $50.
So to put it basically: the cost of the dining plan is the cost of one full table-service meal per night, on average.
Disney is willing to give me a deal on dining! If I commit to buying and paying for one full table-service meal per night and person of my entire reservation, they will give me a full counter service meal, a snack, and a refillable mug for free! The counter service meal costs about $15 (on average), the snack costs $3 (on average), and the mug costs $2 per night ($15 cost of the mug, including tax, divided by a 7 night trip). That's about $20 in freebies per night...or 38.8% in freebies.
The 38.8% in freebies of the DDP sure does beat the pants off the 20% that you get from TIW. However, the bigger discount comes with the bigger restrictions of the DDP.
The numbers, for me, are skewed even more in favor of DDP because before you realize any benefit from TiW, you have to have eaten enough to make up the cost of the card itself. At $100, you have to have spent $500 in food before you break even. That $500 is the cost of almost 10 nights of the DDP.
Assumptions:
The numbers above do assume that you make full use of the DDP. Not everyone gets a soda/juice/coffee/etc with their meal. Not everyone wants dessert. Not everyone eats that much food. I understand that. The DDP isn't for everyone. I always get soda and I will almost always want either an appetizer or dessert. The DDP forces me towards a dessert, but I am willing to accept that for the bigger discount.
The numbers above also assume that you aren't concerned with price while on vacation AND that your dining preferences include an equal mix of expensive and cheap dining options. The numbers can skew higher if you eat only at the most expensive single credit dining options, can skew lower if you use dining credits for breakfast, and some people don't mind budgeting food on vacation. I tend to eat at the places I want to and I am not overly concerned with price. If you shop around, you can eat very well for a lot less than $50 per table-service meal. Again, this is why the DDP isn't for everyone.
Other Notes:
I didn't take in to account the cost of gratuity, since you should tip no matter what. The DDP does give you the freedom to decide on a lower tip, should you feel the service was bad enough to not be deserving of 18%. You can always add more, but I consider 18% to be the point at which I start and I work up to about 25% for excellent service and down to 15% for mediocre service. I won't go below 15% unless you simply ignore me all night. TiW basically forces your minimum to be 18%, so you do get some inflexibility in that regards.
The above calculations also only take the adult DDP in to account, as we are a couple of DINKs. It doesn't apply to kids. My understanding is that if your kids are in the range for the kids DDP, there can be even bigger savings.
The other thing to take into account for TiW is alcohol: TiW includes alcohol while DDP does not. I am not a big drinker... I'll have a few drinks on vacation, but not enough to make TiW worth it. On a vacation, my alcohol bill will total about $100.
Finally, This is just my take on DDP, TiW, and how they apply to myself and my dining habits. Everyone's dining habits are different and you should apply your own analysis.