Both Fujifilm XQ1 and Nikon P7800 have 12.0 MP resolution sensors but Fujifilm XQ1's sensor is 2/3" (8.8 x 6.6 mm ) and Nikon P7800'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 Nikon P7800.
Below you can see the XQ1 and P7800 sensor size comparison.
As seen above, Fujifilm XQ1 has a 1.4x Larger sensor area than Nikon P7800. 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.