Either you hold on to the car long enough to have positive equity, or you dump it now and take the loss (and learn an expensive lesson).
At this point it's a sunk cost so really up to you. You will get more money private party, however sometimes it's harder to secure a buyer/financing for newer cars with a higher cost.
I'm not sure what car you have or how much it is owed, but depending on what the price you are considering for a used vehicle, it *may* make more sense to just keep your car and pay it off with the cash you'd use for the "new" used car.