Here is my 2 cents from someone who had purchased his first ever AP AND the TIW (in August 2016 with 3 of us). Knowing the way we eat and the places we go, (and our party size of 3 to 5), it definitely made sense for us. I like Mike's math above. I look at it as it saving me 2% and not having to worry about the tip.
To Kristin's point, many discounts are also available for AP holders as well and more so this year in celebration of their anniversary. That said, however, we found that in our trip in November 2016 (with 5 of us) that many of the discounts for AP were at places that wouldn't do TIW, and those that TIW would only give 10% if you were only an AP (if they offered any AP discount). Since I am a non-Florida resident, I cannot get TIW without the AP. So anywhere I purchased anything I always asked if the AP (or TIW at food places) provided any discount for us. In the end it did pay off.
I do have to make a correction of what Mike said. The "Upfront" cost (again for a Non-Resident) is $150 but you must be an AP holder. ($175 for Florida residents but no AP requirement). A second member is $50 in case you are dining "Separately" (particularly with an "Adult" child). Also each TIW is good for 10 guests on ONE bill and MUST be paid for by the TIW holder. As Mike said, the DO check ID. (or at least compare name on CC with name on TIW). If you will have groups OVER 10, then it's probably worthwhile to have a second TIW to cover up to 20 people (Ugh!)
Another added bonus is that TIW discount covers Alcohol (if that's your thing) where the AP discounts do not.
We had the
DDP on one of our trips (We bought it not the free one). It's "Roughly" $65/person/day. It's worth it if you are a "Foodie" type person. But if you have kids (older than 10) who are fussy about their eats, you will almost NEVER get your moneys worth out of their price. Convenience? Yes, but not monetarily. Even as an adult, it's hard to get the value out of them. As I recall we got 1 TS, 1QS, 1 Snack per day (plus the mug). We had more food then we knew what to do with. In the hotter months you don't want to eat that much either, so that's another thing to consider.
It's nice though to use the TS to make the reservations and not worry. Also remember, the Dining Plan does NOT include the TIP (unless it's for one of those meals like Ohana where Tip is included in the cost). So if the choice is between DDP and TIW? I think it doesn't take as long to get the value out of TIW as it would to try and get it out of the DDP (on a PURELY FINANCIAL basis and not "Convenience" that is a value you need to decide on).