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 S5 II has a 24.0MP Full frame (35.6 x 23.8 mm ) sized CMOS sensor and features Venus Engine processor.
Panasonic S5 II's sensor provides 10MP 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.
One other difference between these two cameras that is worth mentioning is that Panasonic S5 II's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the ZR3 and S5 Mark II sensor size comparison.
As seen above, Panasonic S5 II has a 30.6x Larger sensor area than Panasonic ZR3. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.