Both Fujifilm X-T20 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-T20'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-T20 and A77 II sensor size comparison.
Fujifilm X-T20 and Sony A77 II have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.