Ricoh GR III has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor . On the other hand, Fujifilm X-E4 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-E4 and Ricoh GR III 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 GR III and X-E4 sensor size comparison.
Ricoh GR III and Fujifilm X-E4 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 Ricoh GR III has 8% larger pixel area compared to Fujifilm X-E4, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.