Panasonic GH2 has a
16.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine FHD processor. On the other hand, Olympus E-M5 III has a
20.0MP Four Thirds (17.4 x 13 mm ) sized MOS sensor and features TruePic VIII processor.
Below you can see the GH2 and E-M5 Mark III sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic GH2 and Olympus E-M5 III Cameras
Panasonic GH2 and Olympus E-M5 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.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Panasonic GH2
or the
Olympus E-M5 III ,
including hyperfocal distance.