Panasonic G5 has a
16.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine VII FHD processor. On the other hand, Olympus E-M1 III has a
20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic IX processor.
One other difference between these two cameras that is worth mentioning is that Olympus E-M1 III'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 G5 and E-M1 III sensor size comparison.
Panasonic G5 and Olympus E-M1 III 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.