I have had 10 Feldenkrais-sessions and they were a very unique experience. One thing that is unique to it is that it is very hard to put in words what exactly the benefit is, at least for beginners. The general consensus in my class was that it was it was great even though the people couldn't name why.
My 2 cents on it: Feldenkrais is very sublte and gentle. It allows you to experience your body in a new way, free of preformed conceptions or ideas, and to experience your blockades very gently. It reconnects you with your body on a very basic level, it's almost more like you give your body the opportunity to experience itself and the things it can and can't do. At least for beginners, the effects seem to be below the threshold of consciousness.
I'd say it differs a lot from the above mentioned martial arts. I can well see it having spiritual benefits, but i would see it mainly as a great way of "resetting" the body, establishing a link with it, before starting more elaborate practices.