Both Fujifilm XQ1 and Panasonic FH1 have 12.0 MP resolution sensors but Fujifilm XQ1's sensor is 2/3-inch (8.8 x 6.6 mm ) and Panasonic FH1's sensor is 1/2.3-inch (6.08 x 4.56 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 Panasonic FH1.
Below you can see the XQ1 and FH1 sensor size comparison.
As seen above, Fujifilm XQ1 has a 2.1x Larger sensor area than Panasonic FH1. 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.