Both Fujifilm X-H1 and Sony A77 II have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
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 A77 II sensor size comparison.
Fujifilm X-H1 and Sony A77 II have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture.