Sony A100 has a 10.0MP APS-C (23.6 x 15.8 mm ) sized CCD sensor . 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.
Fujifilm X100S's sensor provides 6MP more than Sony A100's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
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 moire occurring in certain scenes.
Below you can see the A100 and X100S sensor size comparison.
Sony A100 and Fujifilm X100S 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 Sony A100 has 59% larger pixel area compared to Fujifilm X100S, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.