Both FujiFilm F300EXR and Canon D20 have 12.0 MP resolution sensors but FujiFilm F300EXR's sensor is 1/2-inch (6.4 x 4.8 mm ) and Canon D20's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since FujiFilm F300EXR'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 Canon D20.
Below you can see the F300EXR and D20 sensor size comparison.
FujiFilm F300EXR and Canon D20 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.