Both Fujifilm F550 EXR and Casio EX-H30 have 16.0 MP resolution sensors but Fujifilm F550 EXR's sensor is 1/2-inch (6.4 x 4.8 mm ) and Casio EX-H30's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Fujifilm F550 EXR'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 Casio EX-H30.
Below you can see the F550 EXR and EX-H30 sensor size comparison.
Fujifilm F550 EXR and Casio EX-H30 have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.