I think, it would always save time, effort & money to relaunch a retiring/ailing business if you are confident that you can turn it around, compared to starting on its own. The absolute start of a startup is a very lonely track to follow initially. You would also need to find and build a team of people who share your belief in your product. You can save all that effort & time by picking up an existing business.
It also depends on what sort of product/service idea you have in mind. If its not done before then you may be better off starting from scratch and if it or its closely resembling avatars are done before then finding out a business who is not doing it well and relaunching them may be a better option.