I get this question a lot. Should I take a tour, or should I just do it by myself? Well, that's a tricky one since there are so many factors involved.
First, how long a vacation do you have? Some tours pack so much into one go, that you get to see so many things, but in a flash of an eye. If you are just there to see the sights and move on, well, you are in luck, many tours offer this. But if you prefer to linger and take your time, then, I am guessing you would not like to be rushed to get back on that tour bus while you keep your travel companions waiting.
Is one cheaper over the other? Well, yes and no. I've done both, and somehow, they come out almost the same. Since I always go for the cheaper alternative in all my travels, I search for the budget tours, the budget accommodation, etc. The good side to budget tours is sometimes, they get really good deals on nice hotels, but are just too far away from the city center. But don't fret, if the city has a good public transportation system, then, I feel this is not going to be a hindrance. The tour will often give you a list of their hotels, so you can always do a bit of research and find out a bit about your accommodations before booking. Aside from having big discount on hotels, tours have good deals on airfare, entrance fees and guides. If you do things on your own, the chances of getting a group rate will be not as good if you are just a few traveling together.
Do you get to see more in tours? Fortunately, many tour operators have an idea what their customers want to see and what are the main attractions of each destination, so you will have a good chance of seeing most of the tourist spots. The downside? You may not have a true "local" experience since there will hardly be enough time for this.
So my suggestion would be, first pick the places you want to see and study the possibilities, if you can do things on your own or not. If you feel you don't want to be bothered by the details of planning a trip, then, let someone do that for you. That is what travel agents are for, right?
Happy travels!