Both Fujifilm X-T1 IR and Fujifilm S9800 have 16.0 MP resolution sensors but Fujifilm X-T1 IR's sensor is APS-C (23.6 x 15.6 mm ) and Fujifilm S9800's sensor is 1/2.3 (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 Fujifilm S9800.
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 S9800 sensor size comparison.
As seen above, Fujifilm X-T1 IR has a 13.1x Larger sensor area than Fujifilm S9800. 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.