Both Fujifilm F770EXR and Nikon S9300 have 16.0 MP resolution sensors but Fujifilm F770EXR's sensor is 1/2-inch (6.4 x 4.8 mm ) and Nikon S9300's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Fujifilm F770EXR'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 Nikon S9300.
Below you can see the F770EXR and S9300 sensor size comparison.
Fujifilm F770EXR and Nikon S9300 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.