Both FujiFilm S2500HD and Fujifilm X100 have 12.0 MP resolution sensors but FujiFilm S2500HD's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm X100's sensor is APS-C (23.6 x 15.8 mm ).
Since Fujifilm X100's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to FujiFilm S2500HD.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the S2500HD and X100 sensor size comparison.
As seen above, Fujifilm X100 has a 13.3x Larger sensor area than FujiFilm S2500HD. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.