In general, an older used vehicle will cost less to insure since it is normally worth less than a brand new car. Also parts and repair costs tend to be lower for a used car compare to a new car and thus if the car must be repaired after an accident the expense should be less for the insurer to fix the used car.
If the new car though is a mid-size family sedan it may cost less than say a used Jaguar to insure. So it will depend on the type of vehicle as well as the age of it. Collision-damage costs are also one of the main factors in differentiating the cost of insuring one type of car over another. To a lesser extent, you also want to look at how attractive the car is to thieves, if a car is popular to thieves and often stolen it may be higher to insure, whether it is new or used.
If you are searching for a car to buy and are trying to decide between a new or older vehicle, you can get an automobile insurance quote on each vehicle to see what the price difference would be for each to be insured.