Both Nikon S4000 and Fujifilm XQ1 have 12.0 MP resolution sensors but Nikon S4000's sensor is 1/2.3-inch (6.17 x 4.55 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 Nikon S4000.
Below you can see the S4000 and XQ1 sensor size comparison.
As seen above, Fujifilm XQ1 has a 2.1x Larger sensor area than Nikon S4000. 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.