Canon ELPH 150 IS has a 20.0MP 1/2.3' (6.17 x 4.55 mm ) sized CCD sensor and features Digic 4+ processor. On the other hand, Leica M9-P has a 18.0MP Full frame (36 x 24 mm ) sized CCD sensor .
One other difference between these two cameras that is worth mentioning is that Leica M9-P's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the ELPH 150 IS and M9-P sensor size comparison.
Sensor Size and Resolution Comparison image of Canon ELPH 150 IS and Leica M9-P Cameras
As seen above, Leica M9-P has a 30.8x Larger sensor area than Canon ELPH 150 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.