Panasonic G9 has a 20.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . On the other hand, Panasonic GF3 has a 12.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine FHD processor.
Panasonic G9's sensor provides 8MP more than Panasonic GF3'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 G9 and GF3 sensor size comparison.
Panasonic G9 and Panasonic GF3 have the same 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 Panasonic GF3 has 67% larger pixel area (18.74µm2 vs 11.16µm2) compared to Panasonic G9, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.