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, Canon S95 has a 10.0MP 1/1.7" (7.44 x 5.58 mm ) sized CCD sensor and features Digic 4 processor.
Canon ELPH 150 IS's sensor provides 10MP more than Canon S95'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 S95 sensor size comparison.
As seen above, Canon S95 has a 1.5x 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.