How much power is generated from a typical solar-powered watch?
There are two main factors which will affect the power you can get from solar.


How much power the solar radiate on your watch's solar panel. Per this link, in summer day, 40 degree latitude, there will be 600W/m^2, and in winter, there will be 300W/m^2.
The efficiency of your solar panel. This depends on many factors, typical may be less than 15%, according to this link.


Assume a 600W/m^2 solar power and a 15% efficiency, 1 cm^2 solar panel:

$$
600W/m^{2} \times 0.15 \times 1 cm^2 \approx 10mW
$$