Both Nikon S9100 and Fujifilm XF1 have 12.0 MP resolution sensors but Nikon S9100's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm XF1's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm XF1'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 S9100.
Below you can see the S9100 and XF1 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon S9100 and Fujifilm XF1 Cameras
As seen above, Fujifilm XF1 has a 2.1x Larger sensor area than Nikon S9100. 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.