Sony H20 has a
10.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor . On the other hand, Sony HX300 has a
20.0MP 1/2.3-inch (6.16 x 4.62 mm ) sized BSI-CMOS sensor .
Sony HX300's sensor provides 10MP 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 HX300 sensor size comparison.
Sony H20 and Sony HX300 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.