Both Olympus FE-5020 and FujiFilm F80EXR have 12.0 MP resolution sensors but Olympus FE-5020's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and FujiFilm F80EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since FujiFilm F80EXR'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 Olympus FE-5020.
Below you can see the FE-5020 and F80EXR sensor size comparison.
Olympus FE-5020 and FujiFilm F80EXR 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.