If you can get more money by selling the car to someone such as on Craigslist or anywhere else then selling the car would be a better idea.
If the old car is Junk and not worth fixing up then selling the car to a Junkyard that buys scrap cars and sells parts of of them can get you more money than just a junkyard buying the car for scrap by the ton.
Right now scrap cars are $30.00 per ton here so it would be better to sell it to a scrap car buyer who sells auto parts off them or donate the car instead.
With current scrap prices you might get $30.00 to $50.00 for the scrap car depending on how much it weighs.
So right now the better option would be to donate the car to a charity who can then sell the car for scrap or they will fix it and sell it to someone.
Or someone may buy the car from charity and then fix it themselves.
If you donate a car to charity you can get a good tax deduction on your income tax so in that case you'd benefit from the donated car more than selling it for scrap.
However you might get more cash for the car if you sell it to someone directly.