Nikon P7100 has a 10.0MP 1/1.7" (7.44 x 5.58 mm ) sized CCD sensor and features Expeed C2 processor. On the other hand, Nikon P7800 has a 12.0MP 1/1.7" (7.44 x 5.58 mm ) sized BSI-CMOS sensor .
Below you can see the P7100 and P7800 sensor size comparison.
Nikon P7100 and Nikon P7800 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 P7100 has 20% larger pixel area compared to Nikon P7800, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.