Both Sony RX10 III and Panasonic G9 have 20.0 MP resolution sensors but Sony RX10 III's sensor is 1″ (13.2 x 8.8 mm ) and Panasonic G9's sensor is Four Thirds (17.3 x 13 mm ).
Since Panasonic G9'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 Sony RX10 III.
One other difference between these two cameras that is worth mentioning is that Panasonic G9'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 RX10 III and G9 sensor size comparison.
As seen above, Panasonic G9 has a 1.9x Larger sensor area than Sony RX10 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.