Panasonic ZS1 has a 10.0MP 1/2.5-inch (5.744 x 4.308 mm ) sized CCD sensor . On the other hand, Fujifilm F800EXR has a 16.0MP 1/2-inch (6.4 x 4.8 mm ) sized EXRCMOS sensor and features EXR processor.
Fujifilm F800EXR's sensor provides 6MP more than Panasonic ZS1'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.
Below you can see the ZS1 and F800EXR sensor size comparison.
As seen above, Fujifilm F800EXR has a 1.2x Larger sensor area than Panasonic ZS1. 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.