Both Sony A6000 and Fujifilm X-H1 have 24.0 MP resolution sensors but Sony A6000's sensor is APS-C (23.5 x 15.6 mm ) and Fujifilm X-H1's sensor is APS-C (23.5 x 15.6 mm ).
Since Fujifilm X-H1'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 Sony A6000.
One other difference between these two cameras that is worth mentioning is that Fujifilm X-H1's sensor doesn't have an 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 moiré occurring in certain scenes.
Below you can see the A6000 and X-H1 sensor size comparison.
Sony A6000 and Fujifilm X-H1 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.