Sony A6000 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz X processor. On the other hand, Sony NEX-6 has a 16.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz processor.
Sony A6000's sensor provides 8MP more than Sony NEX-6'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 A6000 and NEX-6 sensor size comparison.
Sony A6000 and Sony NEX-6 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 Sony NEX-6 has 49% larger pixel area (22.87µm2 vs 15.28µm2) compared to Sony A6000, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.
DxOMark Sensor Scores
Both Sony A6000 and Sony NEX-6 sensors have been tested by DxoMark. DxoMark scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Of the two cameras that we are comparing, A6000 has scored 82, 4 points higher than NEX-6.