Panasonic S1 has a 24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor. On the other hand, Sony A7S has a 12.0MP Full frame (35.8 x 23.9 mm ) sized CMOS sensor and features Bionz X processor.
Panasonic S1's sensor provides 12MP more than Sony A7S'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 S1'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 S1 and A7S sensor size comparison.
Panasonic S1 and Sony A7S 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.
DxOMark Sensor Scores
Both Panasonic S1 and Sony A7S sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, S1 has scored 95, 8 points higher than A7S.