Both Casio EX-Z450 and Fujifilm X100 have 12.0 MP resolution sensors but Casio EX-Z450's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm X100's sensor is APS-C (23.6 x 15.8 mm ).
Since Fujifilm X100'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 Casio EX-Z450.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the EX-Z450 and X100 sensor size comparison.
As seen above, Fujifilm X100 has a 13.3x Larger sensor area than Casio EX-Z450. 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.