Sony A7 III has a 24.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz X processor. On the other hand, Canon R has a 30.0MP Full frame (36 x 24 mm ) sized CMOS sensor . Canon R's sensor provides 6MP more than Sony A7 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.
Below you can see the A7 III and R sensor size comparison.
Sony A7 III and Canon R have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.