Both Nikon AW120 and Fujifilm F800EXR have 16.0 MP resolution sensors but Nikon AW120'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 Nikon AW120.
Below you can see the AW120 and F800EXR sensor size comparison.
Nikon AW120 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.