Samsung NX1 has a 28.0MP APS-C (23.5 x 15.7 mm ) sized BSI-CMOS sensor and features DRIMe 5 processor. On the other hand, Olympus E-M1 III has a 20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic IX processor.
Samsung NX1's sensor provides 8MP more than Olympus E-M1 III'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 similarity between these two cameras is that both Olympus E-M1 III and Samsung NX1 sensors lack anti-alias (Low-Pass) filters. 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 NX1 and E-M1 III sensor size comparison.
As seen above, Samsung NX1 has a 1.6x Larger sensor area than Olympus E-M1 III. 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.