There are advantages and disadvantages on both sides, of course. What does this mean? It means that there is no such thing as a right answer. All you can do is evaluate both methods and see which one will suit you best.
Making a private sale
A private sale implies the fact that you, the owner of the car you are looking to sell, will go through the whole selling process on your own. This will mean that you are willing to invest a great amount of your time and energy into this transaction, but at the same time, your efforts will be rewarded. You will receive more money than going to a dealership.
The first thing you need to do is to put a price on the car. Check the market. There are even some websites such as Car Sales which can do that for you. Just type in the features of your car and they will make a quick financial evaluation of it.
Make sure that the car is clean and that it works perfectly. Most car buyers will want to use it immediately, so it should work perfectly from a mechanical point of view.
Buyers will contact you. They will have questions, and they will require meetings. You need to be available at any given time. Respond fast to their enquiries and stay flexible during driving tests.
Decide which is the lowest price you are willing to take, before starting a negotiation.
If you can afford the time and energy, a private sale can bring you more money, so it is a great option to take into consideration.
Going to a dealership
It is the easiest option. Many people find it as being the most convenient one, and this is why it is more costly. Addressing a dealer when selling the car means that you are willing to get less money from the sale than you would normally get in a private sale.
If you want to sell the car immediately, this is the best option you can get. The downside of the private selling process is that you are at the mercy of the market.
The best thing you can do is to take your car to a dealer that sells related vehicles.
A lot of thought should be put into this decision. Only after all options have been considered should you make a final one.