Both Resorts are gorgeous & with both you'll have all of the benefits of staying on Disney Property like free transportation to the Parks, participation in Extra Magic Hours, complimentary package delivery & so on.
If it does come down to saving money, go for Port Orleans French Quarter. You won't regret it as it's a beautiful resort that is fun for the entire family.
In fact, the last time my family came down to Disney with the Grandparents we stayed at POFQ and it is now the Resort that the Grandparents & our kids asked to stay at next year for our family trip! Our entire family agreed that Port Orleans French Quarter felt like a luxury Disney property, but with a better price tag! We usually stay at Moderate or Deluxe Resorts in Disney.
Some of the perks that we enjoyed while there were connecting rooms with Grandparents, lovely walking trails with immaculate landscaping, taking the ferry to Downtown Disney (huge hit!), a big food court which is important when you need a table for so many people at breakfast, walking to Port Orleans Riverside Resort for dinner at Boatwright's Dining Hall & the peaceful Sassagoula River lazily winding through the property. Oh, & that huge Sea Serpent Water Slide impressed my kids mightily!
Next time we go everyone wants to experience the Horse-Drawn Carriage Rides by the River and fishing at the Ol' Fishin' Hole!
You can't go wrong with either Resort & they are both popular & spectacular in their own ways, but I thought I'd share a little bit of what my group enjoyed in the hopes that it will help you decide! Either way, I hope that you have a fantastic trip with your family full of special memories!