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 ELPH 510 HS has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor .
Canon ELPH 150 IS's sensor provides 8MP more than Canon ELPH 510 HS'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 ELPH 510 HS sensor size comparison.
Canon ELPH 150 IS and Canon ELPH 510 HS 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 ELPH 510 HS has 65% larger pixel area (2.34µm2 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.