Both Nikon S6500 and Fujifilm F600 EXR have 16.0 MP resolution sensors but Nikon S6500's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm F600 EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since Fujifilm F600 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 Nikon S6500.
Below you can see the S6500 and F600 EXR sensor size comparison.
Nikon S6500 and Fujifilm F600 EXR 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.