A chain is made up of a number of links, most of which are generally thinner than a heavy duty rap ring (or we could say just as thick if it makes people feel better). Having one point of reliance, rather than 8-10 in a chain (any of which could fail) is preferred.
I'm not even sure how you rap off of hangers. Care to explain? Do you leave a locker or something? Rig up some sling? In that case, I think it is obvious that this is the worst option. (picture is of what I call a heavy duty rap ring)