Sony A9 III has a
24.6MP Full frame (35.6 x 23.8 mm ) sized Global Shutter 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.
Another difference between these two cameras is that Sony A9 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 A9 Mark III and R1 sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A9 III and Canon R1 Cameras
Sony A9 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 A9 III
or the
Canon R1 ,
including hyperfocal distance.