Only you can decide this one. There are pros and cons for both.
First of all, you need to realize that there is a difference between cost and value. One travel plan may cost less than another, but not deliver the same travel value in the end. I know that sounds a little strange, but there are certain unseen perks that may be associated with a tour that you would not experience going independently.
I tried my first Rick Steves tour last year, after years of fun and successful independent travel. I found that I really enjoyed the tour and received a value from it that I did not receive from independent travel. I would have to say that I think the two major plus factors for a well run tour is that the logistics are carefully thought out and optimized and that the educational value of the guide(s) is not comparable to just using a guide book.
Logistics is way more than just someone figuring out where to stay and how to get from place to place, although that can be quite helpful. It is also knowing the time of day to arrive at a location, how long to plan to stay there, and special arrangements such as a catered picnic lunch in a D-day museum to maximize the time available to enjoy the D-Day sights. The tour was far better organized than I do as an independent traveler and I am actually a very good travel planner.
The educational value of the guide is very hard to quantify into dollars and cents. I learned so much and I learned it through enjoyable and engaging presentations by both our tour guide and the series of local guides that would lead us through their speciality areas.
The con of a tour can be that the tour itinerary may not match with what you are interested in seeing. You need to carefully decide what your top interests and goals are for this trip. Does it match with a tour offerring or would you be "settling" and seeing places that you are not interested in?
Since my first Rick Steves Tour last summer I have done an independent trip to Ireland, will do an independent trip to London, and have signed up for the Rick Steves Switzerland tour in August. Travel doesn't have to be just independent or just a tour. You need to determine for your particular family what matches your needs best.
We had 8 teenagers on our tour and they had a blast. I am completely unsure why a previous poster felt that the tour and teenagers weren't a match, unless of course, they have never been on a tour.
I do caution, however, of thinking only in terms of dollars and cents, since this doesn't adequately equate to the value of the experiences.