Both Nikon P500 and Olympus 1 have 12.0 MP resolution sensors but Nikon P500's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Olympus 1's sensor is 1/1.7-inch (7.44 x 5.58 mm ).
Since Olympus 1'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 1 sensor size comparison.
As seen above, Olympus 1 has a 1.5x 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.