Olympus SP-565UZ has a 10.0MP 1/2.33" (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, Panasonic G7 has a 16.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . Panasonic G7's sensor provides 6MP more than Olympus SP-565UZ'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 SP-565UZ and G7 sensor size comparison.
As seen above, Panasonic G7 has a 8.1x Larger sensor area than Olympus SP-565UZ. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.