Nikon 1 J4 has a
18.0MP 1' (13.2 x 8.8 mm ) sized CMOS sensor and features Expeed 4 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.
One other difference between these two cameras that is worth mentioning is that Olympus E-M1 III's sensor doesn't have an 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 1 J4 and E-M1 III sensor size comparison.
As seen above, Olympus E-M1 III has a 1.9x Larger sensor area than Nikon 1 J4. 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.