Both Panasonic FP1 and Fujifilm XQ1 have 12.0 MP resolution sensors but Panasonic FP1's sensor is 1/2.3-inch (6.08 x 4.56 mm ) and Fujifilm XQ1's sensor is 2/3-inch (8.8 x 6.6 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 FP1.
Below you can see the FP1 and XQ1 sensor size comparison.
As seen above, Fujifilm XQ1 has a 2.1x Larger sensor area than Panasonic FP1. 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.