It depends. Efficiency depends on the furnace, more so than the fuel. Some gas furnaces are as high as 97% efficient. Natural gas prices and oil prices vary greatly because of the vagaries of supply and demand.
In general, oil is used where natural gas is not available. Gas is clean burning, relatively odor free, you get charged as you use it, there is a constant supply.
With oil, you get odor from the oil, odor from the burning oil. If the burner is not operating perfectly, you can get soot in the chimney and ducts. You have to have a supplier deliver when you need oil. The suppliers may be busy or may be short on supply just when you need it. You have to store the oil in or near your home, in a tank. It is a potential hazard.
If I had to pay more for the fuel, I would still choose natural gas.