Casio Pro EX-F1 has a 6.0MP 1/1.8" (7.144 x 5.358 mm ) sized CMOS sensor . On the other hand, Nikon P7800 has a 12.0MP 1/1.7" (7.44 x 5.58 mm ) sized BSI-CMOS sensor . Nikon P7800's sensor provides 6MP more than Casio Pro EX-F1'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 Pro EX-F1 and P7800 sensor size comparison.
Casio Pro EX-F1 and Nikon P7800 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.