Canon SX20 IS has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features Digic 4 processor. On the other hand, Canon G12 has a 10.0MP 1/1.7-inch (7.44 x 5.58 mm ) sized CCD sensor and features Digic 4 processor.
Below you can see the SX20 IS and G12 sensor size comparison.
As seen above, Canon G12 has a 1.5x Larger sensor area than Canon SX20 IS. 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.