Nikon P7800 has a 12.0MP 1/1.7" (7.44 x 5.58 mm ) sized BSI-CMOS sensor . On the other hand, Fujifilm X-T10 has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS sensor and features EXR Processor II processor.
Below you can see the P7800 and X-T10 sensor size comparison.
As seen above, Fujifilm X-T10 has a 8.9x Larger sensor area than Nikon P7800. 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.