Ricoh CX6 has a 10.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CMOS sensor and features Smooth Imaging Engine IV 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.
Fujifilm F800EXR's sensor provides 6MP more than Ricoh CX6's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the CX6 and F800EXR sensor size comparison.
Ricoh CX6 and Fujifilm F800EXR have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.