Canon ELPH 350 HS has a 20.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features DIGIC 4+ processor. On the other hand, Casio EX-10 has a 12.0MP 1/1.7" (7.44 x 5.58 mm ) sized CMOS sensor and features Exilim Engine HS 3 processor.
Canon ELPH 350 HS's sensor provides 8MP 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 350 HS and EX-10 sensor size comparison.
As seen above, Casio EX-10 has a 1.5x Larger sensor area than Canon ELPH 350 HS. 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.