Fujifilm S3 Pro has a
6.0MP APS-C (23 x 15.5 mm ) sized CCD sensor . On the other hand, Nikon S4000 has a
12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features Expeed C2 processor.
Nikon S4000's sensor provides 6MP more than Fujifilm S3 Pro'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 S3 Pro and S4000 sensor size comparison.
As seen above, Fujifilm S3 Pro has a 12.7x Larger sensor area than Nikon S4000. 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.