The S100 and HX9V are very different cameras.
The S100 is an enthusiast compact, with a larger 1/1.7" sensor and "only" 12 megapixels. It also has a very bright, f/2.0 lens with a short 24-120mm equivalent focal range. It has lots of different control options, and it can shoot "RAW" images for the person who wants total flexibility using a photo editing program. Basically, a compact designed for someone who may already have a DSLR and wants the same control over exposure, but wants a pocketable second camera.
The HX9V is a travel camera. It has a smaller 1/2.3" sensor and 16 megapixel. It has a very wide 24-384mm equivalent focal range, but a dimmer lens; it does not work as well in low light without resorting to a technical "trick." The Sony has less user-defined control options, favoring pre-programmed smart and scene modes instead. It is designed for someone that mostly just wants to "point and shoot," letting the camera figure out exposure.