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, Panasonic LX10 has a
20.0MP 1″ (13.2 x 8.8 mm ) sized BSI-CMOS sensor .
Another difference between these two cameras is that Fujifilm X100S'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 X100S and LX10 sensor size comparison.
As seen above, Fujifilm X100S has a 3.2x Larger sensor area than Panasonic LX10. 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.