Both Nikon P500 and Fujifilm X10 have 12.0 MP resolution sensors but Nikon P500's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm X10's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm X10'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 Nikon P500.
Below you can see the P500 and X10 sensor size comparison.
As seen above, Fujifilm X10 has a 2.1x Larger sensor area than Nikon P500. 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.