Both Olympus XZ-10 and Fujifilm XF1 have 12.0 MP resolution sensors but Olympus XZ-10's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm XF1's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm XF1'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-10.
Below you can see the XZ-10 and XF1 sensor size comparison.
As seen above, Fujifilm XF1 has a 2.1x Larger sensor area than Olympus XZ-10. 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.