I would say; try to sell it yourself first, you will make more money for sure.
When you ask yourself this question you need to have some consideration for other factors, do you have the time to list your car for sale and meet people to test drive and haggle over the price, selling a car on your own is a hassle and it takes time and it may be a process, so you need to make sure that you have the time to consider when you decide to sell your car yourself, however, if you have the time you will probably make more money than trading it in.
Trading in your car may be convenience, but if you have the time to allocate so you should always try selling your car on your own, give it a try, you may be lucky and land a buyer quickly and make few hundred if not couple thousands more depend on what car you are selling.
When you trade in your car to the dealer they try to take it for as low as possible which is understandable, even when you hear commercial on the radio about getting $5000 over the trade in value for your car when you trade it in is just a radio commercials, rest assured when the dealer advertise that they will pay you more for your trade they know very well they will make this money back from you with profit over it, if you don’t believe this so you are just a good naive person.
When it gets to the car business always keep in mind one rule, if it sounds to good to be true it is not true!
Bottom line, try to sell your car on your own and you may be able to have more cash that you can you on your next car purchase this cash should give you a better position walking into the dealer to buy your new car, even if it cost you time to communicate with potential buyers it will definitely get paid for this time.