Fujifilm X-T1 IR has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS II sensor and features EXR Processor II processor. On the other hand, Pentax Q-S1 has a 12.0MP 1/1.7-inch (7.44 x 5.58 mm ) sized BSI-CMOS sensor and features Q Engine processor.
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 X-T1 IR and Q-S1 sensor size comparison.
As seen above, Fujifilm X-T1 IR has a 8.9x Larger sensor area than Pentax Q-S1. 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.