Nikon S9100 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Expeed C2 processor. On the other hand, Sony HX400V has a 20.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Bionz X processor.
Sony HX400V's sensor provides 8MP more than Nikon S9100'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 S9100 and HX400V sensor size comparison.
Nikon S9100 and Sony HX400V 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 Nikon S9100 has 68% larger pixel area compared to Sony HX400V, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.