Fujifilm X-T20 has a
24.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS III sensor and features X-Processor Pro2 processor. On the other hand, Sony A560 has a
14.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz processor.
Fujifilm X-T20's sensor provides 10MP more than Sony A560's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
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 moiré occurring in certain scenes.
Below you can see the X-T20 and A560 sensor size comparison.
Fujifilm X-T20 and Sony A560 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.