Both Fujifilm X20 and Olympus XZ-2 iHS have 12.0 MP resolution sensors but Fujifilm X20's sensor is 2/3-inch (8.8 x 6.6 mm ) and Olympus XZ-2 iHS's sensor is 1/1.7-inch (7.44 x 5.58 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 Olympus XZ-2 iHS.
Below you can see the X20 and XZ-2 iHS sensor size comparison.
As seen above, Fujifilm X20 has a 1.4x Larger sensor area than Olympus XZ-2 iHS. 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.