Olympus TG-610 has a
14.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor and features TruePic III+ processor. On the other hand, Fujifilm F800EXR has a
16.0MP 1/2-inch (6.4 x 4.8 mm ) sized EXRCMOS sensor and features EXR processor.
Below you can see the TG-610 and F800EXR sensor size comparison.
Olympus TG-610 and Fujifilm F800EXR 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.