As far as the trade in goes..
If you trade the vehicle in and you owe more than they offer you, then you have what they call negative equity. That means if they offer you $2000 ( this is just a random number ) less than what you owe, they will simply add that to the new car you are buying. So if the car was $8000 it now becomes $10000 ( again random numbers ).
The pros: You are able to dumb off your old vehicle get into a new one and dont have to come up with the full amount you have in negative equity. You alkso dont have to go thru the process of selling it on your own which you have no idea how to do.
Cons: You are building dept. Cars depreciate, when you go to sell the new vehicle you bout you will take a another loss on it because you over payed for that car in the first place.
Dealerships are middle men. They will buy your car for a reduced price and sell it for a higher one, so if you sell it to them you will take a bigger lose. You can sell it on your own, but again what you find is in todays market is it takes longer to sell a car ( and espeacially a car with known problems ) you have to worry about test drives, people actually having the cash to pay you ( todays economy - nuff said ) you have to smog the vehicle before you sell it, and make sure they switch it over to their name at the dmv or you are still liable for anything they do in that car.
So selling on your own
Pros: You will get more money for your car.
Cons: It takes longer and you have to deal with a little more.
I would right more but I have to go to work. Hope this helps ( and yes I have a back ground in selling cars ).