Nikon D500 has a 21.0MP APS-C (23.5 x 15.7 mm ) sized CMOS sensor and features Expeed 5 processor. On the other hand, Fujifilm X-H1 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features X-Processor Pro processor.
Another similarity between these two cameras is that both Fujifilm X-H1 and Nikon D500 sensors lack anti-alias (Low-Pass) filters. 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 D500 and X-H1 sensor size comparison.
Nikon D500 and Fujifilm X-H1 have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.