Leica Q has a 24.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Maestro II processor. On the other hand, Leica Q2 Monochrom has a 47.0MP Full frame (36 x 24 mm ) sized CMOS sensor .
Leica Q2 Monochrom's sensor provides 23MP more than Leica Q'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 Leica Q2 Monochrom'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 Q Typ 116 and Q2 Monochrom sensor size comparison.
Leica Q and Leica Q2 Monochrom 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 Leica Q has 94% larger pixel area compared to Leica Q2 Monochrom, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.