Both Fujifilm X20 and Canon A1200 have 12.0 MP resolution sensors but Fujifilm X20's sensor is 2/3-inch (8.8 x 6.6 mm ) and Canon A1200's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Fujifilm X20'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 A1200.
Below you can see the X20 and A1200 sensor size comparison.
As seen above, Fujifilm X20 has a 2.1x Larger sensor area than Canon A1200. 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.