Casio EX-Z450 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor . On the other hand, Fujifilm X-M1 has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS I sensor and features EXR Processor II processor.
One other difference between these two cameras that is worth mentioning is that Fujifilm X-M1'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 X-M1 sensor size comparison.
As seen above, Fujifilm X-M1 has a 13.1x 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.