This is just my take on the matter, based on my understanding of what these terms mean:
Prayer implies a duality—One is addressing something or someone outside one’s self. There is the one who’s praying, and the one being prayed to. As a communication, it has content, a message.
Meditation, at least as I practice it, is about transcending duality by bringing attention to bear. At its best, there is no one meditating, and no object of meditation. The idea of separation between the two is let go of. It is often devoid of content; just pure experience. This is useful only in that it accesses the world of seamless wholeness, which is a very illuminating experience. It has no other “use” per se, but that doesn’t mean it’s worthless.
Critical thinking is analytical, which by its very nature breaks experience down conceptually into component parts. This is useful in dealing with the world of things and individuals, but can’t offer any insight into the world of wholeness.