Panasonic ZS3 has a 10.0MP 1/2.3" (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, 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.
Fujifilm X100S's sensor provides 6MP more than Panasonic ZS3's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100S'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 moire occurring in certain scenes.
Below you can see the ZS3 and X100S sensor size comparison.
As seen above, Fujifilm X100S has a 13.5x Larger sensor area than Panasonic ZS3. 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.