Both Fujifilm XQ1 and Casio EX-10 have 12.0 MP resolution sensors but Fujifilm XQ1's sensor is 2/3" (8.8 x 6.6 mm ) and Casio EX-10's sensor is 1/1.7" (7.44 x 5.58 mm ).
Since Fujifilm XQ1'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 Casio EX-10.
Below you can see the XQ1 and EX-10 sensor size comparison.
As seen above, Fujifilm XQ1 has a 1.4x Larger sensor area than Casio EX-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.