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, Nikon P7100 has a
10.0MP 1/1.7-inch (7.44 x 5.58 mm ) sized CCD sensor and features Expeed C2 processor.
Below you can see the P500 and P7100 sensor size comparison.
As seen above, Nikon P7100 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.