Both Panasonic ZS7 and FujiFilm F300EXR have 12.0 MP resolution sensors but Panasonic ZS7's sensor is 1/2.3-inch (6.08 x 4.56 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 Panasonic ZS7.
Below you can see the ZS7 and F300EXR sensor size comparison.
As seen above, FujiFilm F300EXR has a 1.1x Larger sensor area than Panasonic ZS7. 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.