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, FujiFilm F300EXR has a 12.0MP 1/2-inch (6.4 x 4.8 mm ) sized CCD sensor and features EXR processor.
Canon ELPH 150 IS's sensor provides 8MP more than FujiFilm F300EXR's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the ELPH 150 IS and F300EXR sensor size comparison.
Canon ELPH 150 IS and FujiFilm F300EXR have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.