Fujifilm XF1 has a 12.0MP 2/3-inch (8.8 x 6.6 mm ) sized EXRCMOS sensor . On the other hand, Panasonic ZS80 has a 20.0MP 1/2.3 (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Venus Engine processor.
Panasonic ZS80's sensor provides 8MP more than Fujifilm XF1'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 XF1 and ZS80 sensor size comparison.
As seen above, Fujifilm XF1 has a 2.1x Larger sensor area than Panasonic ZS80. 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.