Both Canon SX20 IS and FujiFilm F300EXR have 12.0 MP resolution sensors but Canon SX20 IS's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and FujiFilm F300EXR's sensor is 1/2-inch (6.4 x 4.8 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 SX20 IS.
Below you can see the SX20 IS and F300EXR sensor size comparison.
Canon SX20 IS and FujiFilm F300EXR 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.