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. On the other hand, Fujifilm X-Pro1 has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS I sensor and features EXR Pro processor.
Fujifilm X-Pro2's sensor provides 8MP more than Fujifilm X-Pro1'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.
Another similarity between these two cameras is that both Fujifilm X-Pro1 and Fujifilm X-Pro2 sensors lack anti-alias (Low-Pass) filters. 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 X-Pro2 and X-Pro1 sensor size comparison.
Fujifilm X-Pro2 and Fujifilm X-Pro1 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 X-Pro1 has 50% larger pixel area (23.04µm2 vs 15.34µm2) compared to Fujifilm X-Pro2, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.