Both FujiFilm Z800EXR and Fujifilm XQ1 have 12.0 MP resolution sensors but FujiFilm Z800EXR's sensor is 1/2-inch (6.4 x 4.8 mm ) and Fujifilm XQ1's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm XQ1'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 Z800EXR.
Below you can see the Z800EXR and XQ1 sensor size comparison.
As seen above, Fujifilm XQ1 has a 1.9x Larger sensor area than FujiFilm Z800EXR. 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.