Both Nikon P7800 and Fujifilm X30 have 12.0 MP resolution sensors but Nikon P7800's sensor is 1/1.7" (7.44 x 5.58 mm ) and Fujifilm X30's sensor is 2/3" (8.8 x 6.6 mm ).
Since Fujifilm X30'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 P7800 and X30 sensor size comparison.
As seen above, Fujifilm X30 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.