Leica Q has a 24.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Maestro II processor. On the other hand, Panasonic S1R has a 47.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Venus Engine processor. Panasonic S1R'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.
Another difference between these two cameras is that Panasonic S1R'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 Q Typ 116 and S1R sensor size comparison.
Leica Q and Panasonic S1R 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 Leica Q has 100% larger pixel area compared to Panasonic S1R, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.