Sony RX1R III has a
61.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz XR processor. On the other hand, Canon R1 has a
24.0MP Full frame (36 x 24 mm ) sized Stacked CMOS sensor and features Digic X processor.
Sony RX1R III's sensor provides 37MP more than Canon R1'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.
Another difference between these two cameras is that Sony RX1R III'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 moiré occurring in certain scenes.
Below you can see the RX1R III and R1 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony RX1R III and Canon R1 Cameras
Sony RX1R III and Canon R1 have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Sony RX1R III
or the
Canon R1 ,
including hyperfocal distance.