Both Panasonic ZS7 and FujiFilm Z800EXR have 12.0 MP resolution sensors but Panasonic ZS7's sensor is 1/2.3-inch (6.08 x 4.56 mm ) and FujiFilm Z800EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since FujiFilm Z800EXR'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 Z800EXR sensor size comparison.
As seen above, FujiFilm Z800EXR 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.