Both Sony A7 III and Fujifilm X-H1 have 24.0 MP resolution sensors but Sony A7 III's sensor is Full frame (35.8 x 23.8 mm ) and Fujifilm X-H1's sensor is APS-C (23.5 x 15.6 mm ).
Since Sony A7 III's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Fujifilm X-H1.
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 A7 III and X-H1 sensor size comparison.
As seen above, Sony A7 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.