Sony A390 has a
14.0MP APS-C (23.5 x 15.7 mm ) sized CCD sensor and features Bionz processor. On the other hand, Fujifilm X100S has a
16.0MP APS-C (23.6 x 15.8 mm ) sized CMOS X-TRANS II sensor and features EXR II processor.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100S's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the A390 and X100S sensor size comparison.
Sensor Size and Resolution Comparison image of Sony A390 and Fujifilm X100S Cameras
Sony A390 and Fujifilm X100S 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
Sony A390
or the
Fujifilm X100S ,
including hyperfocal distance.