Sony HX20V has a 18.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features BIONZ processor. On the other hand, 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.
Sony HX20V's sensor provides 6MP more than Casio EX-10'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 HX20V and EX-10 sensor size comparison.
As seen above, Casio EX-10 has a 1.5x Larger sensor area than Sony HX20V. 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.