FujiFilm S2500HD has a
12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized CCD sensor . On the other hand, Fujifilm X-Pro2 has a
24.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS III sensor and features EXR Processor III processor.
Fujifilm X-Pro2's sensor provides 12MP more than FujiFilm S2500HD'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-Pro2'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 S2500HD and X-Pro2 sensor size comparison.
As seen above, Fujifilm X-Pro2 has a 13.1x Larger sensor area than FujiFilm S2500HD. 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.