Both Olympus E-M10 IV and OM System OM-1 II have Four Thirds sized 20.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
One other difference between these two cameras that is worth mentioning is that OM System OM-1 II's sensor doesn't have an 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 E-M10 IV and OM-1 Mark II sensor size comparison.
Sensor Size and Resolution Comparison image of Olympus E-M10 IV and OM System OM-1 II Cameras
Olympus E-M10 IV and OM System OM-1 II 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
Olympus E-M10 IV
or the
OM System OM-1 II ,
including hyperfocal distance.
