Canon SX120 IS has a 10.0MP 1/2.5-inch (5.744 x 4.308 mm ) sized CCD sensor and features Digic 4 processor. On the other hand, Fujifilm X100 has a 12.0MP APS-C (23.6 x 15.8 mm ) sized CMOS sensor and features EXR processor.
One other difference between these two cameras that is worth mentioning is that Fujifilm X100'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 moire occurring in certain scenes.
Below you can see the SX120 IS and X100 sensor size comparison.
As seen above, Fujifilm X100 has a 15.1x Larger sensor area than Canon SX120 IS. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.