Both Fujifilm XF10 and Sony RX1R have 24.0 MP resolution sensors but Fujifilm XF10's sensor is APS-C (23.5 x 15.7 mm ) and Sony RX1R's sensor is Full frame (35.8 x 23.9 mm ).
Since Sony RX1R's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Fujifilm XF10.
One other difference between these two cameras that is worth mentioning is that Sony RX1R'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 XF10 and RX1R sensor size comparison.
As seen above, Sony RX1R has a 2.3x Larger sensor area than Fujifilm XF10. 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.