Fujifilm S1 Pro has a 3.0MP APS-C (23 x 15.5 mm ) sized CCD sensor . On the other hand, Samsung NX1 has a 28.0MP APS-C (23.5 x 15.7 mm ) sized BSI-CMOS sensor and features DRIMe 5 processor. Samsung NX1's sensor provides 25MP more than Fujifilm S1 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.
Another difference between these two cameras is that Samsung NX1's sensor lacks anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moire occurring in certain scenes.
Below you can see the S1 Pro and NX1 sensor size comparison.
Fujifilm S1 Pro and Samsung NX1 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.