Both Canon SD780 IS and Fujifilm XQ1 have 12.0 MP resolution sensors but Canon SD780 IS's sensor is 1/2.3 (6.17 x 4.55 mm ) and Fujifilm XQ1's sensor is 2/3" (8.8 x 6.6 mm ).
Since Fujifilm XQ1'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 SD780 IS.
Below you can see the SD780 IS and XQ1 sensor size comparison.
As seen above, Fujifilm XQ1 has a 2.1x Larger sensor area than Canon SD780 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.