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, Sony H50 has a 9.0MP 1/2.3" (6.17 x 4.55 mm ) sized CCD sensor .
Canon ELPH 350 HS's sensor provides 11MP more than Sony H50'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 H50 sensor size comparison.
Canon ELPH 350 HS and Sony H50 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Sony H50 has 125% larger pixel area (3.13µm2 vs 1.39µm2) compared to Canon ELPH 350 HS, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.