Sony A7S III has a 12.0MP Full frame (35.6 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz XR processor. On the other hand, Panasonic S1H has a 24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor.
Panasonic S1H's sensor provides 12MP more than Sony A7S III'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 III and S1H sensor size comparison.
Sony A7S III and Panasonic S1H 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 Sony A7S III has 99% larger pixel area compared to Panasonic S1H, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.