Fujifilm X-T20 has a 24.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS III sensor and features X-Processor Pro2 processor. On the other hand, Fujifilm X-T10 has a 16.0MP APS-C (23.6 x 15.6 mm ) sized CMOS X-TRANS II sensor and features EXR Processor II processor.
Fujifilm X-T20's sensor provides 8MP more than Fujifilm X-T10'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 difference between these two cameras is that Fujifilm X-T20's sensor lacks 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 moire occurring in certain scenes.
Below you can see the X-T20 and X-T10 sensor size comparison.
Fujifilm X-T20 and Fujifilm X-T10 have 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-T10 has 50% larger pixel area (23.04µm2 vs 15.34µm2) compared to Fujifilm X-T20, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.