Panasonic G2 has a
12.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine HD II processor. 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 G2'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 G2 and E-M1X sensor size comparison.
Panasonic G2 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.