When I read the question I looked closely at the words, "useful" and "banned." I have trained dogs professionally and for a police department and I believe that both of these training aids can be useful in the right hands.
First of all I'd like to change the words here from "choke collar" to "slip collar" and "prong" to "pinch." A choke collar is not intended to "choke" the animal and if it is used as such it is being employed wrong. When used correctly it will slip back to it's open position and not choke the animal.
Also there is a right and a wrong way to put a slip collar on. With the dog by your side the collar should slip down through the hole, not up. In other words it should form a "P" not a "d". This allows the collar to slip back into the opened position after it's pulled and released. If the collar is put on incorrectly, the excess of the chain runs up through the hole and it will become locked in a choking position and not release thereby choking the dog. Dogs have sensitive nerves in their necks not to mention their airway is located there also. Choking a dog with a chain collar can cause irreperable damage.
The "pinch" collar also should be employed lightly and only in extreme cases. Personally I would go to a shock collar before a pinch collar. So yes, both collars can be useful when in the hands of a trained canine handler.
I'm not sure what the person asking the question about banning the collars wants to know. I'm guessing that he or she is referring to government intervention when they say banning. In other words they are asking if the Federal, State or local government should write legislation prohibiting the use of these collars. My answer to that is, "No." I've already explained that in the hands of a professional trainer these collars have their uses, so banning them would take a tried and true training aid away from trainers. I know there are people who use these collars to inflict pain and we have legislation in every state that bans cruelty to animals. I strongly recommend that you get involved if you see a person employing a choke or pinch collar to inflict undue pain on an animal. PLease call the SPCA or local law enforcement.
As far as banning these collars by any canine association you would have to look at their rule book. If a dog is being used to show or trial it generally has had enough training that it wouldn't need a pinch collar. Slip collars are used at shows and generally are made from nylon, not chain.
Of course my basic philosophy is that a well trained dog is a happy one. If the dog is trained properly there is no need for any collar. A nylon harness works just as well if you know what you're doing. Advanced obedience allows you to give commands to your dog off-lead and that is the level every dog owner should strive for. If the dog will respond to the handler off-lead he'll be a pleasure to walk on-lead.