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, Samsung NX mini has a 20.5MP 1" (13.2 x 8.8 mm ) sized BSI-CMOS sensor .
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 NX mini sensor size comparison.
As seen above, Fujifilm X-T20 has a 3.2x Larger sensor area than Samsung NX mini. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.