Casio EX-H20G has a
14.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD 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-H20G and F800EXR sensor size comparison.
Casio EX-H20G 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.