Sony A7S II has a 12.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Bionz X processor. On the other hand, Sony A7 III has a 24.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz X processor.
Sony A7 III's sensor provides 12MP more than Sony A7S II'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 A7S II and A7 III sensor size comparison.
Sony A7S II and Sony A7 III 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
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It 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. Sony A7S II and Sony A7 III sensors have been tested by DxO and the results show that A7 III has a better overall score of 96, 11 points higher compared to A7S II's score of 85.