Sales tax on cars is 10% there?!?!?!? I bet it's not. Sales tax around here is 9% , but on cars it's just 3.5%
Like I said, around here the sales tax is 3.5% on cars. For every $1k in trade-in value, you save 35 in tax savings. Just about the only way trading-in makes sense over selling privately is when the prices are almost exactly the same.
If the trade-in offer is $13k on your old truck, you need to sell it private-party for at least $13,455 to break-even w/ the tax effects. It's still almost certainly a better deal to sell privately.