Both Olympus E-M1 II and Panasonic G9 have 20.0 MP resolution sensors but Olympus E-M1 II's sensor is Four Thirds (17.4 x 13 mm ) and Panasonic G9's sensor is Four Thirds (17.3 x 13 mm ).
Since Olympus E-M1 II's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Panasonic G9.
Another difference between these two cameras is that Panasonic G9's sensor lacks 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 moire occurring in certain scenes.
Below you can see the E-M1 II and G9 sensor size comparison.
Olympus E-M1 II and Panasonic G9 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.