Both FujiFilm AV250 and Fujifilm Z1000EXR have 16.0 MP resolution sensors but FujiFilm AV250's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm Z1000EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since Fujifilm Z1000EXR'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 AV250.
Below you can see the AV250 and Z1000EXR sensor size comparison.
FujiFilm AV250 and Fujifilm Z1000EXR have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.