Fujifilm X-H1 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features X-Processor Pro processor. On the other hand, Olympus E-M1 II has a 20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor.
Another difference between these two cameras is that Fujifilm X-H1'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 moire occurring in certain scenes.
Below you can see the X-H1 and E-M1 II sensor size comparison.
As seen above, Fujifilm X-H1 has a 1.6x Larger sensor area than Olympus E-M1 II. 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.