There are many advantages and disadvantages with binaural beats. One of the major advantages is hemispheric synchronization. Since both hemispheres are required to create the beat within the brain, this method is an excellent way to create greater harmony between areas of the mind typically functioning independently. Binaural beats are also known to have effective hypnotic and relaxing effects.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself.