We are a family of 4, spending 11.5 days in the world. Our plan includes eating breakfast at our rental house most mornings, and carrying sandwiches and bottled water with us to the parks for lunch many times. Mainly, we have one TS per day, with a couple of TS breakfasts thrown in, and some QS lunches. We budgeted $2500 for our food (including the food we will cook and eat at the house) which is $200 per day, or $50 / day / person.
As others have mentioned, free dining is not always a great deal, it depends. In general, the bigger your family, and the more you eat, the better chance you have of making out good on free dining.
We have used free dining many times, always as a family of 4 or 5, and we are pretty heardy eaters. In addition, we were always staying at a moderate resort (POR). If you are a smaller family, or don't eat as much normally, or are staying at a deluxe resort, then there is a good chance you would actually save more money by purchasing your food OOP, buying tickets from a 3rd party, and taking advantage of a room only discount for your stay.
For our upcoming trip, we rented a house off site, for less than it would have cost us to stay at POR, purchased our tickets from a 3rd party, again at a significant savings from buying through Disney, and we will be paying for our dining OOP.