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, Panasonic G9 has a 20.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . Panasonic G9'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.
Another difference between these two cameras is that Panasonic G9's sensor lacks anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the E-PM1 and G9 sensor size comparison.
Olympus E-PM1 and Panasonic G9 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Olympus E-PM1 has 65% larger pixel area compared to Panasonic G9, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.