Panasonic ZS3 has a
10.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, Nikon S3600 has a
20.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor .
Nikon S3600's sensor provides 10MP 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 S3600 sensor size comparison.
Panasonic ZS3 and Nikon S3600 have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.