Either way, you're going to lose a buttload of money. As you probably know, your vehicle probably dropped in value by 30%. If you go to a dealership to trade it in, you're probably looking at closer to 40%, or more, as they will have to resell it.
My suggestion would be to sell it privately for as much as you possibly can. Take it to a dealer, see what they say. If it's acceptable, take their offer and buy the car you want. It's always easier to sell to a dealer -- less legwork for you.