Radiesse Vs. Sculptra for Droopy Mouth and Chin?

Radiesse might be better if you want a more immediate improvement as Sculptra takes a while to make the body produce more collagen as a response to its insertion. You would need more than one treatment with Sculptra probably, several weeks apart, but probably only one treatment with Radiesse.

For the chin, I would absolutely only recommend Radiesse, as it contains a substance (calcium hydroxyapatite) that is identical to bone and teeth and looks and feels more natural. However, I would not recommend the use of this in the sides of the mouth, as it can feel hard and change the appearance of the lips and smile. You would be best suited to use a softer filler in this area such as Restylane, or try Sculptra there. 

FOr the corners ot the mouth droop, I would recommend evolence. It is a long lasting collagen filler. It is firmer and gives nice support to the corners ot the mouth. to enhance the projection of the chin, a so-called non-surigical chin lift I would use radiesse. Sculptra would not be my personnel choice for filling around the mouth and chin, due to the possiblitiy of sculptra nodules or granulomas.

You might want to consider Juvederm Ultra plus or Perlane for the areas you are describing.  If I had to choose between Radiesse vs. Sculptra, I would suggest Radiesse.
Good luck.