Both Casio EX-ZR700 and Fujifilm F800EXR have 16.0 MP resolution sensors but Casio EX-ZR700's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm F800EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since Fujifilm F800EXR'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-ZR700.
Below you can see the EX-ZR700 and F800EXR sensor size comparison.
Casio EX-ZR700 and Fujifilm F800EXR 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.