Both Canon R3 and Sony A9 II have Full frame sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the R3 and A9 Mark II sensor size comparison.
Sensor Size and Resolution Comparison image of Canon R3 and Sony A9 II Cameras
Canon R3 and Sony A9 II 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.
DxOMark Sensor Scores
Both Canon R3 and Sony A9 II sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, R3 has scored 96, 3 points higher than A9 Mark II.
Model
Overall
Color Depth
Dynamic Range
Low-light ISO
Canon R3
96
25.0 bits
14.7 Evs
4086 ISO
Sony A9 II
93
25.0 bits
14.0 Evs
3434 ISO
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
Canon R3
or the
Sony A9 II ,
including hyperfocal distance.