There are two ways to argue this.
One is based on their backgrounds as opposed to any sort of economic policies they are proposing or have proposed. In this view, Romney would be better than Obama since he has been a leader of a major business. This implies that he knows more about the way the free enterprise system works.
The second is based on actual policy proposals. From this point of view, Romney would be better for the economy because he would reduce taxes and government spending. He would also reduce the amount of regulation of the economy. According to some economists, this would increase the aggregate supply in the economy (which more or less means that companies would be able to produce more things) and get the economy going in a way that Obama's more Keynesian (reliant on government spending) policies would not.