Both Olympus SZ-30MR and Fujifilm HS30EXR have 16.0 MP resolution sensors but Olympus SZ-30MR's sensor is 1/2.3-inch (6.17 x 4.55 mm ) and Fujifilm HS30EXR's sensor is 1/2-inch (6.4 x 4.8 mm ).
Since Fujifilm HS30EXR'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 SZ-30MR.
Below you can see the SZ-30MR and HS30EXR sensor size comparison.
Olympus SZ-30MR and Fujifilm HS30EXR have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.