Both Fujifilm X100F and Ricoh GR III have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Another similarity between these two cameras is that both Ricoh GR III and Fujifilm X100F sensors lack anti-alias (Low-Pass) filters. 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 X100F and GR III sensor size comparison.
Sensor Size and Resolution Comparison image of Fujifilm X100F and Ricoh GR III Cameras
Fujifilm X100F and Ricoh GR III 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
Fujifilm X100F
or the
Ricoh GR III ,
including hyperfocal distance.