The advantages of onsite are being in the Disney bubble, terrific theming, not having to drive if you like the onsite transportation (much better than any offsite offerings I know of), extra magic hours, the dining plan, and (sometimes) being close to the parks. Aside from the Swan and Dolphin, any resort within walking distance of a park is Disney's. There are people who stay offsite happily without a car, but they must be a tiny minority; offsite you really need to drive, IMHO. There are, however, hotels and condos on public bus routes where a bus comes by twice an hour from before the parks open until after they close (well, when we've gone), which is a better way to go than most hotel shuttle systems.
Offsite you get more space for the same money. People who stay onsite offseason in one value room and always wait for some kind of deal (
free dining or whatever) may not save money offsite, but people who stay moderate or deluxe usually do. If you get two rooms onsite you can always save money staying offsite in a much nicer place.
Offsite covers everything from cheap hotels to rental homes with splash pools; you can either stay way cheaper than onsite in a comparable-sized situation, or you can spend about the same you would for a value onsite and get a pretty nice place. I think there are a few resorts offsite that match Disney's theming in the sense of spending a lot of time, money, and effort to get the theming right, but Disney keeps the edge because they have such a huge resource to bounce off of. Nobody else has anything to compare to hidden Mickeys or subtle touches like that, because no one else has decades of cartoons and movies and whatnot to work with. (Well, technically I guess Universal does, but they don't go that route.) Some offsite resorts offer pools, lazy rivers, and other water things that outdo anything Disney has.
We love having a kitchen, so for us that's a huge advantage of offsite (DVC kitchens are too small for my crew). I may only make breakfast there, but I can have real eggs, cooked exactly the way I want them, on hot whole wheat toast with real melted butter. Comfort is little things, and that's one of my comforts.
We like condos, don't like hotels for more than a day or two, and haven't tried out a house with a splash pool yet, and probably won't until we're not traveling with my two most sociable kids, who like the opportunity of meeting people at the resort when going swimming and the like. If your comfort is having someone else make your breakfast and someone else clean you room everyday, then a hotel with free breakfast might be a better bet for you.
While there are offsite resorts as close to the parks in drive time as many onsite resorts, some offsite resorts are a fair drive away, which can be a big disadvantage, obviously. But if you choose carefully, you can be as close to the parks offsite as the average Disney resort is.
Most people I know who stay both offsite and on will stay offsite for longer trips and onsite for short ones; even if you're staying in the same kind of unit, offsite offers the larger spaces necessary for longer trips. Sometimes those differences go further; onsite they'll stay in a hotel room and always eat out, while offsite they'll stay in a house or condo and sometimes eat in. Onsite trips they'll spend time enjoying the resort, offsite trips they'll hit the parks every day -- or the other way around!
The pros and cons change a bit depending on how large a group you are, how long you go, etc. Since there are more options offsite, they can vary considerable depending on where you stay offsite. If you've always stayed in a hotel room onsite and switch to a condo off, that's going to be a bigger difference than if you stay DVC and switch to an offsite condo, for instance.
The number of onsite resorts can be overwhelming for newbies, and of course there are far more offsite options. But once you know whether you want house, condo, or hotel, people here can give you some specific recommendations and information.
The downtown Disney hotels, or the Bonnet Creek ones, are both "within the gates", and Wyndham Bonnet Creek pleases many an onsiter making their first foray offsite.
