I've done on-site and off-site. Love them both, but they're different trips:
When we stay on-site, it's go-go-go. We can be quite Commando about the parks -- after all, tickets are expensive, and we want to make the most of our time. We love Disney transportation, and with teens that'd matter to me -- Disney transportation allows them to go here or there (or hit a park earlier or later than you) without your immediate supervision.
In contrast, when we stay off-site, we sleep in more, grill out nice family dinners, and have leisurely afternoons at the pool with the family. We don't have tickets for every day of our stay. Off-site is also significantly less expensive; the condo we're renting for our next trip is 4-bedrooms and a private pool for $75/night (admittedly, that's off-season).
Both are great -- the question is, Which trip do you want?