Both Sony RX1R and Canon G1 X III have 24.0 MP resolution sensors but Sony RX1R's sensor is Full frame (35.8 x 23.9 mm ) and Canon G1 X III's sensor is APS-C (22.3 x 14.9 mm ).
Since Sony RX1R's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Canon G1 X III.
Another difference between these two cameras is that Sony RX1R's sensor lacks 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 moire occurring in certain scenes.
Below you can see the RX1R and G1 X III sensor size comparison.
As seen above, Sony RX1R 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.