The inside diameter of the neck may be different. I just compared two that I have - the opening of the screw top is 20 mm across and the opening of the cork bottle is 18 mm. Also something I never noticed before - the inside walls of the screw top bottle, right where the cork would end up, are not straight.
I reuse cork-top wine bottles over and over. If I get more from the recycling depot, I'll soak them in the pink Sani-Brew, which gets most of them completely clean - and if not, they just go back. The worst thing is getting the old labels off.