Fujifilm X100F has a 24.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS III sensor and features X-Processor Pro processor. On the other hand, Fujifilm X100 has a 12.0MP APS-C (23.6 x 15.8 mm ) sized CMOS sensor and features EXR processor.
Fujifilm X100F's sensor provides 12MP more than Fujifilm X100's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Another similarity between these two cameras is that both Fujifilm X100 and Fujifilm X100F 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 X100F and X100 sensor size comparison.
Fujifilm X100F and Fujifilm X100 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.