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 X100 has a 12.0MP APS-C (23.6 x 15.8 mm ) sized CMOS sensor and features EXR processor.
Canon ELPH 150 IS's sensor provides 8MP more than Fujifilm X100'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.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100'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 moire occurring in certain scenes.
Below you can see the ELPH 150 IS and X100 sensor size comparison.
As seen above, Fujifilm X100 has a 13.3x 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.