Nikon S630 has a
12.0MP 1/2.3-inch (6.08 x 4.56 mm ) sized CCD sensor . On the other hand, Nikon S3700 has a
20.0MP 1/2.3' (6.17 x 4.55 mm ) sized CCD sensor and features Expeed C2 processor.
Nikon S3700's sensor provides 8MP more than Nikon S630'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 S630 and S3700 sensor size comparison.
Nikon S630 and Nikon S3700 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.