We have been 8 times and have stayed off site all but one of those years. The year we stayed off site is why we won't stay off site again. Now, we are also a family of 3 so the cost isn't as much a difference for us. The more in your party, the higher the cost difference is.
To us, the advantages for on site are:
Location, location, location - yes, there are hotels, resorts, that are close to Disney, but once you get off Disney property, even going one mile can make a difference. We take a break every day at the parks and go back to our resort to rest or swim. We stay at the moderates and the location is still much better than off site. Now, again, this depends on how busy it is when you are down there. During off season when it isn't busy, the traffice off site isn't as bad. But, even a slightly busy time can reap havoc on the traffic.
Atmosphere - we love the theming of the Disney resorts. They are extremely relaxing and very quiete. We love them at night after getting back from the parks.
Transportation - We always drive, so we have our car and drive to most of the parks. The MK is the only one that we take the bus. But, it is very easy to get around in WDW in a car and the bus is there if we don't feel like driving. It is also nice if your party consist of people who want to go to different places at different times. When I have to drive, being on property makes it much less stressful and it is my vacation too.
Perks - Extended hours for resort guests, if going during very busy time, guaranteed entereance to the parks, packages delivered back to your resort from the parks. Disney service.
The biggest advantages for staying off site just don't apply to our family. We are a family of three, sometimes four if we take a friend of our sons, so we don't need the larger accomodations you can get off site. Also, me or my wife aren't going to cook on vacation, so having a kitchen isn't a plus for us. If we travel with extended family, it is a requirement of mine that they have their own place anyway. I don't live with them at home, I'm not living with them on my vacation.
If we needed the extra room, we would probably rent DVC points and get a one bedroom or two bedroom at Old Key West.
Really, it is just a matter of what is going to be important for you and your family. Figure out what is your highest priorities and that will tell you whether on site or off site is best for you.