The former could get you a hulk of a Austin coupe that's been rusting out in the open for 50 years.
Most cars are somewhere in between.
Price is a touchy subject, so I will just post a sort of running score here of ads, sales etc. If you are buying a project your job is going to be much easier if you don't have to spend a fortune in dead end phone calls, fruitless trips, and etherial leads trying to find the right tail lights for your car. Never mind that sixty years of owners have been adding and subtracting parts, wrecking it, leaving it out in the rain and so on. Also, transporting these things all over the place is not all that easy. After that it's up to you.