Nikon D90 has a
12.0MP APS-C (23.6 x 15.8 mm ) sized CMOS sensor . On the other hand, Fujifilm X-Pro1 has a
16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS I sensor and features EXR Pro processor.
One other difference between these two cameras that is worth mentioning is that Fujifilm X-Pro1'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 D90 and X-Pro1 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon D90 and Fujifilm X-Pro1 Cameras
Nikon D90 and Fujifilm X-Pro1 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
Nikon D90
or the
Fujifilm X-Pro1 ,
including hyperfocal distance.