IMHO-- You can screw new over old, but you really don't know where to screw.. You have no studs to go by.., You could screw into a wire or a pipe, and then it would be a possible disaster..
Its a few hundred dollars more to pull the old stuff off and start with clean studs.. You can see the framing and see if there are other problems when you have it open..
For taping its all the same, but usually there is less waviness to the ceiling when its new drywall. If there is waves or humps your taper will end up by spending more time and using more materials to make it flat. Better to start right, rather than doing a cover job.
Glenn S. Berlow, Author