Ricoh GXR Mount A12 has a 12.0MP APS-C (23.6 x 15.7 mm ) sized CMOS sensor . On the other hand, Fujifilm X100S has a 16.0MP APS-C (23.6 x 15.8 mm ) sized CMOS X-TRANS II sensor and features EXR II processor.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100S's sensor doesn't have an anti-alias (Low-Pass) filter. 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 GXR Mount A12 and X100S sensor size comparison.
Ricoh GXR Mount A12 and Fujifilm X100S 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.