Nikon P300 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Expeed C2 processor. On the other hand, Panasonic ZS40 has a 18.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CMOS sensor and features Venus Engine processor.
Panasonic ZS40's sensor provides 6MP more than Nikon P300'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 P300 and ZS40 sensor size comparison.
Nikon P300 and Panasonic ZS40 have the same 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 Nikon P300 has 49% larger pixel area compared to Panasonic ZS40, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.