Both FujiFilm S2500HD and Fujifilm X10 have 12.0 MP resolution sensors but FujiFilm S2500HD's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm X10's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm X10'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.
Below you can see the S2500HD and X10 sensor size comparison.
As seen above, Fujifilm X10 has a 2.1x 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.