This is really a pretty situational question. I have had good success selling vehicles privately, but those were mostly more heavily modified performance cars (Corvettes, GTOs, etc). I have also had success selling to Carmax - I recently got $5k more from them ($40k) than any other dealer would offer on my wife's Explorer. The dealer offers were $35k, so even in Texas with the tax credits of 6.25%, I still netted an extra $2,812.50 by selling to Carmax (over trading it in to the dealer).
I traded my '21 Raptor when I got rid of it because the Ford dealer offered me a fair value, and then I saved all the sales tax on my Tremor ($3,768 in tax savings). So the questions for you are: what are the tax laws in your state - is there a savings by trading? In some states, the answer to that is no. And secondly, will your dealer offer you a fair trade value based on the market and not what you paid? For instance, if you paid MSRP, would they offer you more than that in trade? Some dealers just can't bring themselves to do that, but the current market on a '21 Raptor IS more than MSRP.