One of the points about growing green manure is it does take nitrogen and other things out of the soil as well as the atmosphere, stores them then releases them back into the soil when they break down after cutting and digging in. The storage is one of the important things as this stops the goodness leeching away into the soil, especially over winter, when it rains. When you use farm manure, it loses a lot of the goodness over the winter period through leeching.
Other benefits are it keeps weeds at bay and if left to flower, attracts important insects to the plot.
Be careful though as you do have to make sure you use it within your rotation.
Also there is nothing wrong with using both farm and green, and the green doesn't have to be in your beds for long periods of time, it just depends on what you use.