Some dogs are more stubborn than others, and if you're having better results with a prong collar, then it's obviously a good choice for you.
However, it sounds like your doggie might not understand the rules of being on a leash. You said that when you use a choke chain that your dog will pull to the point of coughing--that's very normal for a dog that does not realize that as the owner, it should obey your rules. I don't know if you've ever watched the show "the dog whisperer" but the guy gives really good advice for how to teach your dogs not to run after cars/chase other animals/etc when it comes to being on a leash. If you can convey to your dog that it is to be totally obedient to you when it is on the leash, you can go back to a choke/normal collar while the dog is on the leash--esp if you're feeling guilty over the prong collar. Getting a professional dog trainer to help you would definitely be a good thing because in cases where a very stubborn dog is involved, sometimes it can be painful to see the dog struggle for dominance on the leash, and they will struggle to the point of almost suffocating themselves. My boyfriend has a pitbull/rottweiler mix, and when we broke her to a leash, it was a very difficult proccess because she DID NOT want to behave. However, after a few weeks of training, and a lot of dicipline, she is now absolutely wonderful, and we no longer have troubles with her chasing cars or the neighborhood animals--mainly cats and squirrels. But like I said, it was a very painful process for us to watch her fight the leash, and we had a lot of rough times-thus the professional dog trainer.
Best of luck to you and your doggie!!