Canon IXUS 165 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 SX130 IS has a
12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features Digic 4 processor.
Canon IXUS 165's sensor provides 8MP more than Canon SX130 IS'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 IXUS 165 and SX130 IS sensor size comparison.
Canon IXUS 165 and Canon SX130 IS 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 SX130 IS has 65% larger pixel area (2.34µm2 vs 1.41µm2) compared to Canon IXUS 165, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.