Both Sony A6000 and Fujifilm X-T20 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 A6000 and X-T20 sensor size comparison.
Sony A6000 and Fujifilm X-T20 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.