There are many advantages to a free market economy. They range from the moral issues to the practical issues. We will deal mainly with the practical ones.
Unprecedented innovation - Free markets are wrought with inventions and the capital to research them. Countries classified as having a free market have been responsible for the vast majority of inventions since the 19th century.
Very high-income mobility - This means that under a free market system it is easier to move around income brackets. It is just easier to become rich or poor when you are left to your own devices as opposed to a controlled economy where resources are allocated by the government.