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. On the other hand, 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.
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.
One other difference between these two cameras that is worth mentioning is that Fujifilm X-T20'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 moire occurring in certain scenes.
Below you can see the X-T10 and X-T20 sensor size comparison.
Fujifilm X-T10 and Fujifilm X-T20 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-T10 has 50% larger pixel area compared to Fujifilm X-T20, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.