When To Sell Privately
If there is no sales tax in your area (lucky you!), the trade-tax advantage is out of the equation. If you are trading something lightly used, chances are you will make more money if you sell it private party, via Craigslist or eBay or some other method. Just keep in mind that you will most likely deal with tire-kickers and low ball offers from people who aren't really serious buyers. I suggest you get a number from your dealership first so you can decide whether or not those private party offers are worth your time.
If you don't have a low mile cream puff to hand over to the dealer, but rather something that has seen some wear and is maybe only worth a few grand at best, private sale may be your best bet. Also, if you have a car that has a following or is "in-demand" private sellers may offer top dollar, while dealerships are just going to run it through their "trade evaluator" and spit out a number.
Of course if your ride isn't worth a lot of money you don't want to spend a fortune marketing it only to make a few hundred dollars. Craigslist is the go-to for listings like these, but you would be surprised how cheap some of the other third party listing sites can be. Cars.com will give you a free 30 day listing with five photos. Autotrader has a basic four-week, three photo package for $25; you can upgrade and add nine photos for an extra $10. eBay Motors is around $60 for a 7-day listing, and final value fees may apply if you're not a regular seller.
When To Trade
In addition to that tax benefit, trading your car to the dealership has two big advantages. First, it is convenient you drop one car off and pick another car up. Many folks don't have the luxury of holding on to a car to sell after they have already bought something, and they may not be able to sell a car before picking up their next ride.
Also, if a buyer is upside-down on their loan, this makes it almost impossible to sell privately. Dealerships have the ability to roll that balance into the next loan or lease.
The key thing here is to be realistic regarding your trade value. Have a look at the private and dealership listings for your same car, see what the numbers are. Use tools like NADA.com, Kelley Blue Book, and Edmund's True Market Value to get a "ballpark" number on what you can expect.
Keep in mind most dealers offer "wholesale auction price" and often the demand for your particular vehicle in a certain area will impact your value. Also, remember that if you have been in an accident no matter how minor, if it is on the vehicle history report you're going to take a hit in your resale value.