You'll get 1 to 2 thousand $ more by selling it outright than trading it in to a dealership, or selling it to a place like carmax.
If you are unfamiliar with all this, I would think a private sale would be a bit much for you.
Yes, you'll lose a bunch of $ trading it in on a lesser car. The difference between what you owe and what the dealer is willing to pay for it will be added to the loan of your "new" lesser car.
But either way, private sale or trade, you'll be losing money in the end.
Stick with what you have if you can.
My speeding isn't the problem. It's the Slow Folks ahead of me that cause accidents!