Both Panasonic LF1 and Nikon S8100 have 12.0 MP resolution sensors but Panasonic LF1's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Nikon S8100's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Panasonic LF1'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 S8100.
Below you can see the LF1 and S8100 sensor size comparison.
As seen above, Panasonic LF1 has a 1.5x Larger sensor area than Nikon S8100. 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.