Both Nikon S6100 and Fujifilm X-M1 have 16.0 MP resolution sensors but Nikon S6100's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm X-M1's sensor is APS-C (23.6 x 15.6 mm ).
Since Fujifilm X-M1'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 S6100.
One other difference between these two cameras that is worth mentioning is that Fujifilm X-M1's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the S6100 and X-M1 sensor size comparison.
As seen above, Fujifilm X-M1 has a 13.1x Larger sensor area than Nikon S6100. 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.