Both Canon A1200 and Canon G15 have 12.0 MP resolution sensors but Canon A1200's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Canon G15's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Canon G15'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 A1200.
Below you can see the A1200 and G15 sensor size comparison.
As seen above, Canon G15 has a 1.5x Larger sensor area than Canon A1200. 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.