Both Olympus TG-850 iHS and Olympus TG-870 have 16.0 MP resolution sensors but Olympus TG-850 iHS's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Olympus TG-870's sensor is (1/2. ).
Since Olympus TG-850 iHS'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-850 iHS and TG-870 sensor size comparison.
As seen above, Olympus TG-850 iHS 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.