I have done both. About half my trips are offsite, and about half my trips are on.
For our family, there isn't a huge difference between them. We don't care about pre-paying for food, and usually spend about the same as or less than the
DDP costs just eating what, where, and when we want. We avoid EMHs whether we are onsite or off, and find the crowds to be lower that way. We always get a rental car, and drive ourselves to most rope-drops to avoid the uncertainty of the buses.
There are two differences we notice. First, it is sometimes nice to let someone else do the driving---usually on Epcot nights when we want to have a second margarita in World Showcase. Second, for *some* Disney resorts, the location is really nice. For example, I liked BWV's Epcot-area location. I also liked VWL's spot on Bay Lake. On the other hand, OKW could have been anywhere, and was comparable to Bonnet Creek.
That said, when I travel with my kids, we absolutely require separate sleeping spaces for the adults and the kids, preferably with a locked door to the adult space

rolleyes1). We definitely want (but don't absolutely require) a living area that no one uses for sleeping, so that night owls or early birds don't disturb everyone else. The cost to do these things onsite is about 2-3x the cost to do them offsite for most people. We can use our (non-Disney) timeshares to stay in DVC units for close to our "offsite cost". But, if that were not available to us, we'd stay offsite every single time. Being onsite is a little nicer. It is not a couple-thousand-dollars-for-a-week nicer.