Fujifilm X100V has a 26.0MP APS-C (23.5 x 15.6 mm ) sized BSI-CMOS sensor and features X-Processor Pro 4 processor. On the other hand, Ricoh GR III has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor .
Another similarity between these two cameras is that both Ricoh GR III and Fujifilm X100V 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 X100V and GR III sensor size comparison.
Fujifilm X100V and Ricoh GR III 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 (15.28µm2 vs 14.12µm2) compared to Fujifilm X100V, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.