Yes, it would matter. If Wade was primarily concerned with the tax effect, he should give the car to his daughter and let her sell it. Conveniently, the limit on how much one can give without paying federal taxes on that gift (other than to charity), is $13,000. This means wade will pay no tax when he gifts the car to his daughter. If he sells it himself, he will need to pay tax on the gain he realizes on the sale of the car, since he will have made a profit on the sale.
His daughter, when she sells the car, will also have to recognize the gain on the sale of the vehicle. However, she is apparently in a much lower income bracket than Wade, and thus may pay even less tax on her 13,000 gain than Wade would have paid on his $3600 profit.