Both Olympus TG-870 and Fujifilm F770EXR have 16.0 MP resolution sensors but Olympus TG-870's sensor is (1/2. ) and Fujifilm F770EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since Fujifilm F770EXR's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Olympus TG-870.
Below you can see the TG-870 and F770EXR sensor size comparison.
As seen above, Fujifilm F770EXR has a infx 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.