Both Olympus SP-565UZ and FujiFilm HS10 have 1/2.3-inch sized 10.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the SP-565UZ and HS10 sensor size comparison.
Sensor Size and Resolution Comparison image of Olympus SP-565UZ and FujiFilm HS10 Cameras
Olympus SP-565UZ and FujiFilm HS10 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 SP-565UZ
or the
FujiFilm HS10 ,
including hyperfocal distance.