Canon ELPH 510 HS has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor . On the other hand, Canon G9 X has a 20.0MP 1' (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features DIGIC 6 processor.
Canon G9 X's sensor provides 8MP more than Canon ELPH 510 HS'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 ELPH 510 HS and G9 X sensor size comparison.
As seen above, Canon G9 X has a 4.1x Larger sensor area than Canon ELPH 510 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.