Both Canon G1 X III and Fujifilm X100F have APS-C sized 24.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100F'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 G1 X III and X100F 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.