Both Panasonic G9 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.
Another similarity between these two cameras is that both OM System OM-1 II and Panasonic G9 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 G9 and OM-1 Mark II sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic G9 and OM System OM-1 II Cameras
Panasonic G9 and OM System OM-1 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.
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
Panasonic G9
or the
OM System OM-1 II ,
including hyperfocal distance.