Sony H20 has a 10.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor . On the other hand, Panasonic ZS60 has a 18.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CMOS sensor and features Venus Engine processor.
Panasonic ZS60's sensor provides 8MP more than Sony H20'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 H20 and ZS60 sensor size comparison.
Sony H20 and Panasonic ZS60 have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Sony H20 has 80% larger pixel area compared to Panasonic ZS60, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.