I'm currently making a quilt using almost exclusively batiks, and they are certainly no stiffer than normal quilting fabrics. They were all bought from Doughtys and Hannah's Room, and sold as quilting fabrics.
I made a top in a batik last year and it came out beautifully. Think slightly crisp cotton, but not stiff - and I don't think there would normally be any difference between batiks sold for quilting and those sold for dressmaking.