Both Fujifilm X20 and Olympus FE-5010 have 12.0 MP resolution sensors but Fujifilm X20's sensor is 2/3-inch (8.8 x 6.6 mm ) and Olympus FE-5010's sensor is 1/2.3-inch (6.08 x 4.56 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 FE-5010.
Below you can see the X20 and FE-5010 sensor size comparison.
As seen above, Fujifilm X20 has a 2.1x Larger sensor area than Olympus FE-5010. 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.