Panasonic ZS1 has a 10.0MP 1/2.5-inch (5.744 x 4.308 mm ) sized CCD sensor . On the other hand, Fujifilm X-E2 has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS II sensor and features EXR Processor II processor.
Fujifilm X-E2'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 X-E2 sensor size comparison.
As seen above, Fujifilm X-E2 has a 14.9x 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.