Sony RX1 has a 24.0MP Full frame (35.8 x 23.8 mm ) sized CMOS 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.
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 RX1 and NX1 sensor size comparison.
As seen above, Sony RX1 has a 2.3x Larger sensor area than Samsung NX1. 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.