Nikon P7800 has a 12.0MP 1/1.7" (7.44 x 5.58 mm ) sized BSI-CMOS sensor . On the other hand, Sony WX50 has a 16.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features BIONZ processor.
Below you can see the P7800 and WX50 sensor size comparison.
As seen above, Nikon P7800 has a 1.5x Larger sensor area than Sony WX50. 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.