Both Fujifilm XP50 and Olympus SP-610UZ have 1/2.3-inch sized 14.0 MP resolution sensors so sensor size and resolution is not a differentiator between these two cameras.
Below you can see the XP50 and SP-610UZ sensor size comparison.
Sensor Size and Resolution Comparison image of Fujifilm XP50 and Olympus SP-610UZ Cameras
Fujifilm XP50 and Olympus SP-610UZ have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Olympus SP-610UZ has 3% larger pixel area (2.04µm 2 vs 1.98µm 2 ) compared to Fujifilm XP50, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.
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
Fujifilm XP50
or the
Olympus SP-610UZ ,
including hyperfocal distance.