Canon G1 X III has a 24.0MP APS-C (22.3 x 14.9 mm ) sized CMOS sensor and features DIGIC 7 processor. On the other hand, Sony RX1R II has a 42.0MP Full frame (35.9 x 24 mm ) sized BSI-CMOS sensor and features BIONZ X processor.
Sony RX1R II's sensor provides 18MP more than Canon G1 X III'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.
One other difference between these two cameras that is worth mentioning is that Sony RX1R II's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the G1 X III and RX1R II sensor size comparison.
Sensor Size and Resolution Comparison image of Canon G1 X III and Sony RX1R II Cameras
As seen above, Sony RX1R II has a 2.6x Larger sensor area than Canon G1 X III. 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.