Olympus E-M10 IV has a 20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor. On the other hand, Panasonic G1 has a 12.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor .
Olympus E-M10 IV'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 E-M10 IV and G1 sensor size comparison.
Olympus E-M10 IV and Panasonic G1 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.