Starting a business will initially be cheaper than buying one. However, buying a business will allow you to hit the ground running and avoid the years that it can take to get a business to the point where it is profitable.
If you buy a business that has already been operating for a number of years, you have the advantage of knowing the product or service has been tried and tested. Entrepreneurs, though, sometimes thrive on the risk-taking that is involved with starting a business from scratch.
The decision depends on your personality. However, go into starting a business with the knowledge that most new businesses fail. Buying a business will not, though, give you the creative freedom that comes with starting your own business.