Casio EX-10 has a
12.0MP 1/1.7-inch (7.44 x 5.58 mm ) sized CMOS sensor and features Exilim Engine HS 3 processor. On the other hand, Fujifilm X-E2S has a
16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS II sensor and features EXR Processor II processor.
One other difference between these two cameras that is worth mentioning is that Fujifilm X-E2S'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 moiré occurring in certain scenes.
Below you can see the EX-10 and X-E2S sensor size comparison.
As seen above, Fujifilm X-E2S has a 8.9x Larger sensor area than Casio EX-10. 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.