Both Fujifilm X100 and Fujifilm X20 have 12.0 MP resolution sensors but Fujifilm X100's sensor is APS-C (23.6 x 15.8 mm ) and Fujifilm X20's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm X100'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 Fujifilm X20.
Another difference between these two cameras is that Fujifilm X100'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 X100 and X20 sensor size comparison.
As seen above, Fujifilm X100 has a 6.4x Larger sensor area than Fujifilm X20. 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.