Panasonic FZ300 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CMOS sensor and features Venus Engine processor. On the other hand, Canon SX610 HS has a 20.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features DIGIC 4+ processor.
Canon SX610 HS'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 FZ300 and SX610 HS sensor size comparison.
Panasonic FZ300 and Canon SX610 HS 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 68% larger pixel area compared to Canon SX610 HS, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.