Nikon A1000 has a
16.0MP 1/2.3 (6.17 x 4.55 mm ) sized BSI-CMOS sensor . On the other hand, Fujifilm A100 has a
10.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor .
Nikon A1000's sensor provides 6MP more than Fujifilm 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.
Below you can see the A1000 and A100 sensor size comparison.
Nikon A1000 and Fujifilm A100 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 Fujifilm A100 has 59% larger pixel area (2.81µm2 vs 1.76µm2) compared to Nikon A1000, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.