What if you voluntarily give up your car for repossession?

This is only a partial question, but I'll try to answer what I think the full question might have been.

Either way you are generally liable for the difference between the fair market value of the car and the amount remaining on the loan, so there's no real difference there.

However, voluntarily giving up the car before it's forcibly repossessed can avoid some headaches. For one thing, you'll avoid the repossession fees; for another, you have some degree of control over exactly when it happens, allowing you to do things like remove aftermarket upgrades (stereo stystem, alloy wheels, etc) you may have installed and replace them with the original equipment.