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-T3 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-T3 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 moire occurring in certain scenes.
Below you can see the X-H1 and X-T3 sensor size comparison.
Fujifilm X-H1 and Fujifilm X-T3 have 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-T3, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.