Both Sony A6000 and Fujifilm X-T20 have 24.0 MP resolution sensors but Sony A6000's sensor is APS-C (23.5 x 15.6 mm ) and Fujifilm X-T20's sensor is APS-C (23.6 x 15.6 mm ).
Since Fujifilm X-T20'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-T20'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-T20 sensor size comparison.
Sony A6000 and Fujifilm X-T20 have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.