Both FujiFilm F80EXR and Casio EX-10 have 12.0 MP resolution sensors but FujiFilm F80EXR's sensor is 1/2-inch (6.4 x 4.8 mm ) and Casio EX-10's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Casio EX-10'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 F80EXR.
Below you can see the F80EXR and EX-10 sensor size comparison.
As seen above, Casio EX-10 has a 1.4x Larger sensor area than FujiFilm F80EXR. 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.