Panasonic ZS3 has a 10.0MP 1/2.3" (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, Panasonic FH10 has a 16.0MP 1/2.3" (6.08 x 4.56 mm ) sized CCD sensor .
Panasonic FH10'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.
Below you can see the ZS3 and FH10 sensor size comparison.
Panasonic ZS3 and Panasonic FH10 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Panasonic ZS3 has 59% larger pixel area compared to Panasonic FH10, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.