They ARE heavier and not as stiff, either. Also, if you ever take it to a track, most organizations will not let 'verts compete unless they have a hefty roll bar.
As other people mentioned, you can't get much use out of a 'vert in Atlanta because you can only drive it enjoyably during the fall and spring (unless you have allergies). Also, cloth tops will always tear eventually and won't insulate the car as well from heat or cold.
It goes without saying, I vote coupe.