Canon SX420 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 A3000 IS has a
10.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor .
Canon SX420 IS's sensor provides 10MP more than Canon A3000 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 SX420 IS and A3000 IS sensor size comparison.
Canon SX420 IS and Canon A3000 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 A3000 IS has 99% larger pixel area (2.81µm2 vs 1.41µm2) compared to Canon SX420 IS, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.