Fujifilm X100S has a
16.0MP APS-C (23.6 x 15.8 mm ) sized CMOS X-TRANS II sensor and features EXR II processor. On the other hand, Olympus E-M1 II has a
20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor.
Another similarity between these two cameras is that both Olympus E-M1 II and Fujifilm X100S sensors lack anti-alias (Low-Pass) filters. 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 X100S and E-M1 II sensor size comparison.
As seen above, Fujifilm X100S has a 1.6x Larger sensor area than Olympus E-M1 II. 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.