Panasonic ZS3 has a 10.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, Nikon L820 has a 16.0MP 1/2.3-inch (6.16 x 4.62 mm ) sized BSI-CMOS sensor .
Nikon L820'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 L820 sensor size comparison.
Panasonic ZS3 and Nikon L820 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.