Just like in crop rotation, the strengths and weaknesses of the system depend on the choice of the cover crop within the entire system of the field.
By making an informed choice this cover crop can be supportive in a broad range of ecosystem services:
pest control
increase of soil organic matter
enhance soil quality
reduced erosion
increased water quality
More detailed information on this can be found here.
More information on Green manures - implications of economic and environmental benefits on rotational management (AHDB Cereals & Oilseeds) (English)
Do keep an eye on the following:
Cover crops can be annual or perennial. In the first case, the cover crop dies in winter. In the second case the cover crop needs to be destroyed or terminated in spring. More information on this can be found here.
In dairy farming a common practice is to take a cut from the cover crop before destruction in spring. In this way you don’t only take organic matter from the field, but also a huge amount of water. This can have a negative influence on the yield of the main crop.