Both OM System OM-1 II and Olympus E-M1 III have Four Thirds sized 20.0 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 Olympus E-M1 III and OM System OM-1 II 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 OM-1 Mark II and E-M1 III sensor size comparison.
Sensor Size and Resolution Comparison image of OM System OM-1 II and Olympus E-M1 III Cameras
OM System OM-1 II and Olympus E-M1 III 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
OM System OM-1 II
or the
Olympus E-M1 III ,
including hyperfocal distance.