A few other considerations to keep in mind. At least in PA, whether you trade your car in at the time of your new car purchase affects how much sales tax you pay for your new car. For example, if the Model 3 I buy is for $40,000 with no trade in, I pay sales tax on $40,000. If I buy a Model 3 for $40,000 but I trade in my current vehicle for $13,000, then I pay sales tax on $27,000 (sales price minus trade in value = amount on which sales tax is paid). So in this example, trading in my car saves me $780.00 ($13,000 x 6% sales tax). So you have to consider if you can get more than $13,780 for your trade in elsewhere.
Another consideration is to whom you would sell it privately. Most people shopping for a car in the price range of less than $7500 will pay cash. Many people buying cars over $10,000 take a loan. That could affect the transaction in terms of speed and ease.
What also might affect the transaction more is if YOU have a loan on the car. If you do, the buyer would have to give you the $13,000 and wait for you to pay off the loan and receive the title in the mail before you can transfer the title to them so they could title the car and drive it. Often buyers aren't willing to trust a seller through those steps.
Not to mention the time, effort and any costs associated with a private sale.
I've sold cars both ways. For me, I'd rather sell my car to the dealer for a fair price (even if it's not top dollar) just for the convenience factor.
