Panasonic G1 has a
12.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . On the other hand, Olympus E-M1X has a
20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features Dual TruePic VIII processor.
Olympus E-M1X's sensor provides 8MP more than Panasonic G1's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the G1 and E-M1X sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic G1 and Olympus E-M1X Cameras
Panasonic G1 and Olympus E-M1X 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 G1
or the
Olympus E-M1X ,
including hyperfocal distance.