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. On the other hand, Canon IXUS 165 has a
20.0MP 1/2.3' (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 SX130 IS and IXUS 165 sensor size comparison.
Canon SX130 IS and Canon IXUS 165 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 compared to Canon IXUS 165, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.