What Mastershake says. I've looked into it on a car of mine, and that's what I came away with.
Plus transport, and any damage, food, lodging, fuel...and time, too, if you want to supervise your car.
It's easy to incur $3000-$4000 in costs to sell that car through an auction.
And if the guy wants a reserve, and the house charges for that, more $$$.
Obviously, without a reserve, the sale price depends on who's there & if anyone's hot for the car.