Fujifilm X-Pro1 has a
16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS I sensor and features EXR Pro processor. On the other hand, Nikon 1 V3 has a
18.0MP 1' (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 4A processor.
Another difference between these two cameras is that Fujifilm X-Pro1'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 moiré occurring in certain scenes.
Below you can see the X-Pro1 and 1 V3 sensor size comparison.
As seen above, Fujifilm X-Pro1 has a 3.2x Larger sensor area than Nikon 1 V3. 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.