FujiFilm S2500HD has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor . On the other hand, Sony HX300 has a 20.0MP 1/2.3-inch (6.16 x 4.62 mm ) sized BSI-CMOS sensor .
Sony HX300's sensor provides 8MP more than FujiFilm S2500HD'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 S2500HD and HX300 sensor size comparison.
FujiFilm S2500HD and Sony HX300 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.