Both Canon SX20 IS and Canon S100 have 12.0 MP resolution sensors but Canon SX20 IS's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Canon S100's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Canon S100'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 Canon SX20 IS.
Below you can see the SX20 IS and S100 sensor size comparison.
As seen above, Canon S100 has a 1.5x Larger sensor area than Canon SX20 IS. 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.