Olympus E-M1 III has a
20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic IX processor. On the other hand, Panasonic GH3 has a
16.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine VII FHD processor.
Another difference between these two cameras is that Olympus E-M1 III'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 moiré occurring in certain scenes.
Below you can see the E-M1 III and GH3 sensor size comparison.
Olympus E-M1 III and Panasonic GH3 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.