Both FujiFilm F300EXR and Olympus XZ-2 iHS have 12.0 MP resolution sensors but FujiFilm F300EXR's sensor is 1/2-inch (6.4 x 4.8 mm ) and Olympus XZ-2 iHS's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Olympus XZ-2 iHS'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 FujiFilm F300EXR.
Below you can see the F300EXR and XZ-2 iHS sensor size comparison.
As seen above, Olympus XZ-2 iHS has a 1.4x Larger sensor area than FujiFilm F300EXR. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.