Both Ricoh GR III and Sony A77 have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Another difference between these two cameras is that Ricoh GR 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 GR III and A77 sensor size comparison.
Sensor Size and Resolution Comparison image of Ricoh GR III and Sony A77 Cameras
Ricoh GR III and Sony A77 have the same sensor sizes so they will provide same level of control over the depth of field when used with 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
Ricoh GR III
or the
Sony A77 ,
including hyperfocal distance.
