What year is the car, how many miles on it, what's damaged, etc. is what we really need to know. Parting it out will usually make more $$ in the end, unless the entire body is destroyed.
I made a little over $3K parting out my old '85 SS. I kept the motor, trans, rear, and front suspension and sold off everything else. When that car was gone, it was just a body tub with doors, glass, and an empty frame. Nothing left on it. Here's a pic of how it looked before I was done.
When this shot was taken, some of the interior was still in the car, and you can see the trunklid and rear marker lights, as well as the brake booster/master cylinder and some other wiring. That all wound up in my garage and shed before she left.