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, Panasonic LX10 has a 20.0MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor . Panasonic LX10'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 LX10 sensor size comparison.
As seen above, Canon G1 X II has a 2.3x Larger sensor area than Panasonic LX10. 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.