Panasonic G9 has a 20.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . On the other hand, Nikon 1 S1 has a 10.0MP 1-inch (13.2 x 8.8 mm ) sized CMOS sensor .
Panasonic G9's sensor provides 10MP more than Nikon 1 S1'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 moiré occurring in certain scenes.
Below you can see the G9 and 1 S1 sensor size comparison.
Sensor Size and Resolution Comparison image of Panasonic G9 and Nikon 1 S1 Cameras
As seen above, Panasonic G9 has a 1.9x Larger sensor area than Nikon 1 S1. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.