Olympus E-M10 III has a
16.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor. On the other hand, Panasonic GX9 has a
20.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine processor.
One other difference between these two cameras that is worth mentioning is that Panasonic GX9'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 III and GX9 sensor size comparison.
Olympus E-M10 III and Panasonic GX9 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.