Like many others here, we enjoy both experiences. Generally we stay off-site. We own one timeshare in Orlando, and two in Hawaii, so we can stay at our own resort or trade to a different one. Even with only DH and I it is nice to have the space to kick back and relax on a couch, rather than watching TV in bed. If I wake up first, I go out to the living room and read or watch TV there. We like to have coffee and snacks whenever the mood hits, so it's great to be able to go into the kitchen and grab something out of the fridge. I don't usually like going out to breakfast. I prefer the relaxed pace of having my usual light breakfast at the condo like I have at home. Most of the resorts have planned activities, various socials, and fun things to do, as well as tennis, basketball, volleyball, etc, which you don't get at a WDW hotel. We enjoy going to the touristy gift shops and attarctions on 192 and I-Drive. When we stay on-site and never leave WDW, I actually miss "the outside world." The whole Orlando area is a fun place with so much to see and do from outlet malls to dinner shows to other theme parks like Sea World and Universal.
As far as on-site, I am a sucker for themed resorts. I love the Disney resorts, and staying at one is a special treat. I don't need to stay for a week, however, and I can happily enjoy a couple days before or after a timeshare stay, or a quick trip like we are doing in November, which is mostly to stay at the Wilderness Lodge, with only one day at a park. Even when we stay off-site, we usually eat once at the Poly or Animal Kingdom Lodge, and we spend a little time walking around the resorts and enjoying the grounds and the theming. I can totally understand liking to be immersed in the fantasy world of a themed resort, but its a real trade-off to give up a spacious condo with whirlpool bath and all the extra perks. I guess that's why we will always do a bit of both, on-site and off-site so we can have our cake and eat it too!