Both Olympus TG-870 and Fujifilm X-T1 IR have 16.0 MP resolution sensors but Olympus TG-870's sensor is 1/2.3" (6.17 x 4.55 mm ) and Fujifilm X-T1 IR's sensor is APS-C (23.6 x 15.6 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 Olympus TG-870.
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 moire occurring in certain scenes.
Below you can see the TG-870 and X-T1 IR sensor size comparison.
As seen above, Fujifilm X-T1 IR has a 13.1x Larger sensor area than Olympus TG-870. 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.