Leica Q2 has a 47.0MP Full frame (36 x 24 mm ) sized CMOS sensor . On the other hand, Sony A7 III has a 24.0MP Full frame (35.8 x 23.8 mm ) sized BSI-CMOS sensor and features Bionz X processor.
Leica Q2's sensor provides 23MP more than Sony A7 III'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 Leica Q2'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 Q2 and A7 III sensor size comparison.
Leica Q2 and Sony A7 III have almost the same sensor size so none of them has any significant advantage over other in providing control over depth of field when used with same focal length and aperture.
DxOMark Sensor Scores
At Camera Decision, we also look at Dxo Mark sensors when available as we think it is a good indicator of image quality.