Well that's a tough one as both have their pros and cons but anyways lets dwell and analyze both the travel types and try to find the better among the two. Traveling alone is taxing as one copes with language barriers, different cultures and customs as well as unknown surroundings.
Agreed but is not this the motive for most of us? Explore new things and enjoy the uncertainties our travel has to offer? Group travel is more safe in an unknown place. Yet, it also sometimes undermines the reason for our holiday that is sightseeing and actually see the places as one starts to socialize more and is sometimes annoyed of fellow travelers. Further one is always dependent upon the group's schedule and lacks the freedom of independent travel. You are a shopaholic and want to spend a day shopping in Paris but you can not as there is a boring visit to the museums. There are times when group travel offers discounted visits to places where one would not individually go.
What we can do in both the travel types is "Be aware of the place you want to travel". Do your homework properly and get to know the place before you actually reach there. There is no dearth of information on the internet so update yourself well or hire someone to make your stay organized and comfortable. In today's world, customized independent tours are a rage as one can get hotel reservations, local transfers, sightseeing, cruises, self driven cars, onward connections according to their own schedule and tastes. Also it gives you a better opportunity to taste local cuisines as well as one can explore according to one's special interests. I know that all these arguments are individualistic but hope that they help you in choosing a group or a customized independent travel .