Olympus E-PM1 has a 12.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features TruePic VI processor. On the other hand, Olympus E-M1 II has a 20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor. Olympus E-M1 II's sensor provides 8MP more than Olympus E-PM1'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-PM1 and E-M1 II sensor size comparison.
Olympus E-PM1 and Olympus E-M1 II 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.