Casio EX-ZR10 has a
12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Exilim Engine HS processor. On the other hand, Fujifilm F800EXR has a
16.0MP 1/2-inch (6.4 x 4.8 mm ) sized EXRCMOS sensor and features EXR processor.
Below you can see the EX-ZR10 and F800EXR sensor size comparison.
Casio EX-ZR10 and Fujifilm F800EXR 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.