You are definitely paying more for a tour company; that being said, since it's your first time, it may be the way to go. I've traveled to Europe several times, both with groups and without, and I definitely preferred arranging things myself. Tours can be great, but sometimes they try to fit too many "touristy" things in their package, and you miss the true sense of the countries because you are spending so much of your time on the tour's schedule. They show you the main sites of the city, then drop you at a central location or send you on an optional tour and you end up having so little time to do your own thing.
This isn't to say that it wouldn't be a great trip for you. It just depends on your preferred style of travel. I like down time and having those days where we sleep a little later and just relax. I planned our trip to Italy 5 years ago, and it was great... we spent a few days in each location, took the trains between cities, and planned much of the trip as we went, with an idea of the major must sees... the Vatican, several museums, the statue of David, etc.
If you decide you want to plan your own trip, Rick Steves has a series of guidebooks that I have found very helpful in planning. He updates them every year, and he tells you all the tips to save money (buy train tickets in advance, for example), ways to avoid the long lines, the things you should make a priority to see, etc.
Either way, you are sure to have a memorable trip. Enjoy!