Both Fujifilm X100F and Canon G1 X III have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Another difference between these two cameras is that Fujifilm X100F's sensor lacks 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 X100F and G1 X III sensor size comparison.
As seen above, Fujifilm X100F has a 1.1x Larger sensor area than Canon G1 X III. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.