Both Olympus SZ-31MR iHS and Panasonic SZ3 have 1/2.3-inch sized 16.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the SZ-31MR iHS and SZ3 sensor size comparison.
Sensor Size and Resolution Comparison image of Olympus SZ-31MR iHS and Panasonic SZ3 Cameras
Olympus SZ-31MR iHS and Panasonic SZ3 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.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Olympus SZ-31MR iHS
or the
Panasonic SZ3 ,
including hyperfocal distance.