Fujifilm X-H1 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features X-Processor Pro processor. On the other hand, Sony A7S III has a 12.0MP Full frame (35.6 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz XR processor.
Fujifilm X-H1'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.
Another difference between these two cameras is that Fujifilm X-H1'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 X-H1 and A7S III sensor size comparison.
As seen above, Sony A7S III has a 2.3x Larger sensor area than Fujifilm X-H1. 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.