Free dining only saves you the cost of your dining plan. 2016 dining prices, including tax, per night are below.
Quick Service Plan - Usually free to value resorts during free dining:
Ages 10+: $42.77
Ages 3-9: $17.54
Regular Plan - Usually free to moderate and deluxe resorts during free dining:
Ages 10+: $61.82
Ages 3-9: $20.98
2 adults and 2 kids (3-9) staying at Pop Century for 7 nights would save $299.39 per adult and $122.78 per kid for a total of $844.34.
2 adults and 2 kids (3-9) staying at Port Orleans for 7 nights would save $432.74 per adult and $146.86 per kid for a total of $1,159.20.
You really have to compare free dining discounts to those of room discounts to try and figure out the best deal for your traveling group. Usually for deluxe and some moderates, you can save more with a 25-30% off room discount than free dining.
Personally, I have never had the dining plan, as it does not fit the way I normally eat at WDW. I would only be willing to try the dining plan when it is offered for free. So far, any trip I have planned that coincided with Free Dining had better room discounts that saved me more money.