Fujifilm Z900EXR has a
16.0MP 1/2-inch (6.4 x 4.8 mm ) sized EXRCMOS sensor and features EXR 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 Z900EXR and E-M1 III sensor size comparison.
As seen above, Olympus E-M1 III has a 7.4x Larger sensor area than Fujifilm Z900EXR. 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.