Canon G1 X II has a 13.0MP 1.5" (18.7 x 14 mm ) sized CMOS sensor and features Digic 6 processor. On the other hand, Canon G7 X has a 20.0MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor and features DIGIC 6 processor.
Canon G7 X's sensor provides 7MP more than Canon G1 X II'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 G1 X MII and G7 X sensor size comparison.
As seen above, Canon G1 X II has a 2.3x Larger sensor area than Canon G7 X. 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.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Canon G1 X II and Canon G7 X sensors have been tested by DxO and the results show that G7 X has a better overall score of 71, 13 points higher compared to G1 X MII's score of 58.