Both Fujifilm X-T1 IR and Nikon S800c have 16.0 MP resolution sensors but Fujifilm X-T1 IR's sensor is APS-C (23.6 x 15.6 mm ) and Nikon S800c's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Fujifilm X-T1 IR'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 S800c.
Another difference between these two cameras is that Fujifilm X-T1 IR's sensor lacks 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 moiré occurring in certain scenes.
Below you can see the X-T1 IR and S800c sensor size comparison.
As seen above, Fujifilm X-T1 IR has a 13.1x Larger sensor area than Nikon S800c. 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.