Olympus TG-870 has a 16.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features TruePic VII 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 TG-870 and P7800 sensor size comparison.
As seen above, Nikon P7800 has a 1.5x Larger sensor area than Olympus TG-870. 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.