Panasonic ZR3 has a 14.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor and features Venus Engine HD II processor. On the other hand, Panasonic ZS80 has a 20.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Venus Engine processor.
Panasonic ZS80's sensor provides 6MP more than Panasonic ZR3'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 ZR3 and ZS80 sensor size comparison.
Panasonic ZR3 and Panasonic ZS80 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.