Canon S120 has a 12.0MP 1/1.7" (7.44 x 5.58 mm ) sized BSI-CMOS sensor and features Digic 6 processor. On the other hand, Canon SX410 IS has a 20.0MP 1/2.3" (6.17 x 4.55 mm ) sized CCD sensor and features DIGIC 4+ processor. Canon SX410 IS's sensor provides 8MP more than Canon S120'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 S120 and SX410 IS sensor size comparison.
As seen above, Canon S120 has a 1.5x Larger sensor area than Canon SX410 IS. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.