Both Ricoh GR III and Sony RX1R have 24.0 MP resolution sensors but Ricoh GR III's sensor is APS-C (23.5 x 15.6 mm ) and Sony RX1R's sensor is Full frame (35.8 x 23.9 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 Ricoh GR III.
One other difference between these two cameras that is worth mentioning is that Sony RX1R'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 moire occurring in certain scenes.
Below you can see the GR III and RX1R sensor size comparison.
As seen above, Sony RX1R has a 2.3x Larger sensor area than Ricoh GR 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.