Canon G12 has a 10.0MP 1/1.7-inch (7.44 x 5.58 mm ) sized CCD sensor and features Digic 4 processor. On the other hand, Canon SX600 HS has a 16.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features DIGIC 4+ processor.
Canon SX600 HS's sensor provides 6MP more than Canon G12'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 G12 and SX600 HS sensor size comparison.
As seen above, Canon G12 has a 1.5x Larger sensor area than Canon SX600 HS. 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.