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 A2200 has a 14.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features DIGIC 4 with iSAPS technology processor.
Canon ELPH 150 IS's sensor provides 6MP more than Canon A2200'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 A2200 sensor size comparison.
Canon ELPH 150 IS and Canon A2200 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Canon A2200 has 42% larger pixel area (2.01µm2 vs 1.41µm2) compared to Canon ELPH 150 IS, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.