Both Canon G16 and Canon SD970 IS have 12.0 MP resolution sensors but Canon G16's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Canon SD970 IS's sensor is 1/2.3-inch (6.17 x 4.55 mm ).
Since Canon G16's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Canon SD970 IS.
Below you can see the G16 and SD970 IS sensor size comparison.
As seen above, Canon G16 has a 1.5x Larger sensor area than Canon SD970 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.