Both Fujifilm X-E3 and Sony A77 have 24.0 MP resolution sensors but Fujifilm X-E3's sensor is APS-C (23.6 x 15.6 mm ) and Sony A77's sensor is APS-C (23.5 x 15.6 mm ).
Since Fujifilm X-E3'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 A77.
Another difference between these two cameras is that Fujifilm X-E3'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 moiré occurring in certain scenes.
Below you can see the X-E3 and A77 sensor size comparison.
Fujifilm X-E3 and Sony A77 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.