Is independent travel better than a group tour? I think that depend on what you want from your vacation. Both of them have their advantages and disadvantages. Group travel is cheaper and more convenient, while independent travel offers much more freedom.
Traveling with a tour group is cheaper than traveling independently. Because travel agents offer package deal, we can purchase a tour that includes the flight, hotels and food. If you travel independently you have to book everything separately, and it will charge you more many and take oyu more time. Tour groups are also more convenient. If you book a tour, you don't have to spend hours to read guidbook and surf the interent. This convenience continues during you vacation, like you will have a tour guide to meet you at the airport, have someone to carry your luggage, moreover on a tour, you won't have to worry about getting lost or how to speak different language. In an on the other hand you have complete freedom to choose where you go and what you do, you don't have to feel like a sheep that is being herded by the flag-waving tour leader. You can even follow your mind and spontaneously change your plans as you travel.
What kinds travel would you like, I think that is depends on what you want from your vacation. If you don't want to spend more time to surf the interent for information, you can choose a tour group that agent will handle all the details and makes all decisions for you. If you like an exciting adventure travel, or value your freedom and don't mind paying more or searching for affordable flights and meals, then independent travel is for you.