Sony H300 has a 20.0MP 1/2.3" (6.17 x 4.55 mm ) sized CCD sensor and features Bionz(R) processor. On the other hand, Panasonic FZ300 has a 12.0MP 1/2.3" (6.17 x 4.55 mm ) sized CMOS sensor and features Venus Engine processor.
Sony H300's sensor provides 8MP more than Panasonic FZ300'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 H300 and FZ300 sensor size comparison.
Sony H300 and Panasonic FZ300 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 Panasonic FZ300 has 65% larger pixel area (2.34µm2 vs 1.41µm2) compared to Sony H300, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.