Sony A100 has a 10.0MP APS-C
(23.6 x 15.8 mm ) sized CCD sensor . On the other hand, Fujifilm X-M1 has a 16.0MP APS-C
(23.6 x 15.6 mm ) sized CMOS X-TRANS I sensor and features EXR Processor II processor.
Fujifilm X-M1'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 X-M1'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 A100 and X-M1 sensor size comparison.
Sony A100 and Fujifilm X-M1 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.