Fujifilm X-A7 has a
24.0MP APS-C (23.5 x 15.7 mm ) sized CMOS sensor . 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 X-A7 and E-M1 III sensor size comparison.
As seen above, Fujifilm X-A7 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.