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, Fujifilm X-Pro3 has a
26.0MP APS-C (23.5 x 15.6 mm ) sized BSI-CMOS sensor and features X-Processor 4 processor.
Another similarity between these two cameras is that both Fujifilm X-Pro3 and Fujifilm X-H1 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 moiré occurring in certain scenes.
Below you can see the X-H1 and X-Pro3 sensor size comparison.
Fujifilm X-H1 and Fujifilm X-Pro3 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Fujifilm X-H1 has 8% larger pixel area compared to Fujifilm X-Pro3, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.