Both Panasonic G9 and Olympus E-M1 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 Olympus E-M1 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 moire occurring in certain scenes.
Below you can see the G9 and E-M1 II sensor size comparison.
Panasonic G9 and Olympus E-M1 II have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.