Panasonic ZS7 has a
12.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor and features Venus Engine HD II processor. On the other hand, Sony H300 has a
20.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features Bionz(R) processor.
Sony H300's sensor provides 8MP more than Panasonic ZS7'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 ZS7 and H300 sensor size comparison.
Panasonic ZS7 and Sony H300 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.