Panasonic ZS3 has a
10.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, Sony HX10V has a
18.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features BIONZ processor.
Sony HX10V's sensor provides 8MP 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 HX10V sensor size comparison.
Panasonic ZS3 and Sony HX10V 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.