Generally speaking you are always better off to sell yourself. You are pretty sure to get more money this way compared to just trading in.
CarMax is a good option to try. They generally offer more than the dealers, and at least you have another offer to compare to whatever the dealer offers you in trade. I sold my last vehicle to them, and I'm so glad I did. They beat the dealers best offer by almost 2 grand. And almost no hassle involved, very easy process.
Selling yourself has a few headaches involved, which are well known. Low ball offers, meeting strangers, tire kickers, and just the general hassle of the paperwork and stress of receiving payment. Again, these should all come with a payoff of a higher selling price.
As someone else mentioned, find out if your state deducts the trade in from the sale price before calculating sales tax. California does not, but some states do. That could be thousands of dollars in taxes saved, so it makes a big difference in the decision.