I've done Italy both with a tour group and on our own. (I also went to Greece w/ a tour group)
Pros for a tour group: If it's your first time to the country, I think a group is a good way to go. You generally have free time to explore on your own--but you're never going to be sitting around in the hotel room trying to figure out what to do next. Transportation is taken care of--a HUGE plus if you don't really know where you're going. You usually get to skip long lines for major attractions. I think the main thing w/ a group is that it is pretty much worry free. You have someone looking out for you and your best interests, and helping you have a great vacation.
I've not been on a Disney tour, but looking at the hotel choices, and the itenerary, I think it's a fantastic way to go.
Now, Pro- On your own: Vacation can be an exhausting thing. You may wake up and really not want to go to such and such museum. You may want to simply go to a market, sit at a cafe and people watch. You may have off the wall interests that most tour groups don't address (for example, there was a very strange torture museum in a tiny town in Tuscany. My guess is
ABD didn't stop there

) You may have your heart set on a particular hotel that you saw on the Travel Channel. You may hate art museums but love aquariums. Groups don't always have that kind of flexibility.
Like I said--tour groups, esp. high quality ones can be a fantastic and maybe even more importantly, EASY, way to see a new country. Visiting on your own takes a ton of work and planning, but you can tailor it to your own interests. I think ABD puts out a great product, even though it's expensive.