Nikon P500 has a 12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Expeed C2 processor. On the other hand, Olympus SZ-31MR iHS has a 16.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Dual TruePic V processor.
Below you can see the P500 and SZ-31MR iHS sensor size comparison.
Nikon P500 and Olympus SZ-31MR iHS have sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Nikon P500 has 32% larger pixel area compared to Olympus SZ-31MR iHS, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.