Canon RP has a 26.0MP Full frame (35.9 x 24 mm ) sized CMOS sensor and features Digic 8 processor. On the other hand, Sony A7R III has a 42.0MP Full frame (35.9 x 24 mm ) sized BSI-CMOS sensor and features Bionz X processor.
Sony A7R III's sensor provides 16MP more than Canon RP'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 A7R III'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 RP and A7R III sensor size comparison.
Canon RP and Sony A7R III have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Canon RP has 62% larger pixel area compared to Sony A7R III, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.