Both FujiFilm F300EXR and Panasonic TS3 have 12.0 MP resolution sensors but FujiFilm F300EXR's sensor is 1/2-inch (6.4 x 4.8 mm ) and Panasonic TS3's sensor is 1/2.3-inch (6.08 x 4.56 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 Panasonic TS3.
Below you can see the F300EXR and TS3 sensor size comparison.
As seen above, FujiFilm F300EXR has a 1.1x Larger sensor area than Panasonic TS3. 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.