Both Panasonic ZS7 and FujiFilm F80EXR have 12.0 MP resolution sensors but Panasonic ZS7's sensor is 1/2.3-inch (6.08 x 4.56 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 Panasonic ZS7.
Below you can see the ZS7 and F80EXR sensor size comparison.
As seen above, FujiFilm F80EXR 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.