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, FujiFilm Z800EXR has a
12.0MP 1/2-inch (6.4 x 4.8 mm ) sized CCD sensor and features EXR processor.
Canon IXUS 165's sensor provides 8MP more than FujiFilm Z800EXR'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 Z800EXR sensor size comparison.
Canon IXUS 165 and FujiFilm Z800EXR have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.