Fujifilm Z900EXR has a 16.0MP 1/2" (6.4 x 4.8 mm ) sized EXRCMOS sensor and features EXR processor. On the other hand, Olympus SP-565UZ has a 10.0MP 1/2.33" (6.08 x 4.56 mm ) sized CCD sensor . Fujifilm Z900EXR's sensor provides 6MP more than Olympus SP-565UZ'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 Z900EXR and SP-565UZ sensor size comparison.
As seen above, Fujifilm Z900EXR has a 1.1x Larger sensor area than Olympus SP-565UZ. 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.