Both Fujifilm X-H1 and Sony A7 III have 24.0 MP resolution sensors but Fujifilm X-H1's sensor is APS-C (23.5 x 15.6 mm ) and Sony A7 III's sensor is Full frame (35.8 x 23.8 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 X-H1 and A7 III 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.