Pentax Q-S1 has a
12.0MP 1/1.7" (7.44 x 5.58 mm ) sized BSI-CMOS sensor and features Q Engine processor. On the other hand, Pentax K-5 IIs has a
16.0MP APS-C (23.7 x 15.7 mm ) sized CMOS sensor and features Prime II processor.
One other difference between these two cameras that is worth mentioning is that Pentax K-5 IIs'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 moiré occurring in certain scenes.
Below you can see the Q-S1 and K-5 IIs sensor size comparison.
As seen above, Pentax K-5 IIs has a 9.0x 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.