FujiFilm S2800HD has a 14.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor . On the other hand, Sony H300 has a 20.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features Bionz(R) processor.
Sony H300's sensor provides 6MP more than FujiFilm S2800HD's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the S2800HD and H300 sensor size comparison.
FujiFilm S2800HD and Sony H300 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since FujiFilm S2800HD has 44% larger pixel area compared to Sony H300, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.