I come at this from the pet dog training world, not sport. I have done classes using both over the years -- and I've successfully trained pet dogs in basic obedience with both. Having said that, I'm 100% in favor of prong over choke, assuming the handler is properly trained to use the tool.
The prong is honestly gentler and more humane, despite how it looks. It takes a much milder correction to get a dog's attention, and that ultimately means fewer corrections, and I'd rather train without needing a lot of corrections. It fixes pulling almost instantly. I enjoyed the balanced classes that used prongs + treats much more than the older-style classes that used choke chains, and I honestly think the dogs did too.
I think it's also easier for new handlers to learn proper technique with a prong (it's a quick little flick of the wrist, not a yank. In classes, I see newbies picking it up in their first class with a good trainer.
OTOH, I see a lot of people out on the street using choke chains incorrectly ("yank-and-crank," choking the dog). They are not doing the correct "popping" motion. I think that's because it takes a lot more practice to get that popping motion's timing and technique right, in my experience. Or people just buy the tool without getting trained how to use it. If you watch people jerking their dog around, or their dog pulling them and choking itself, they don't know how to use it correctly -- and I honestly see that a lot. You can learn proper technique, but it takes longer, and frankly a little more finesse to do it well. It also takes longer for the corrections to sink in on some stubborn dogs, I think.
The one BIG thing with a prong is that it MUST be properly fitted. The common mistake I see out on the street with prongs is that they're too loose, which has them falling too low. Any trainer who uses them will make sure they're properly fitted at the start of class. I don't think anyone should just go out and buy a prong and try to start using it--it's worth having someone knowledgeable show you how to use it.
I deal with pulling a lot of big, untrained, adolescent dogs out of shelters--dogs who have NO manners, have been stuck in a kennel at a dog pound for weeks without a walk, with tons of pent up energy. I'm a small woman, but I have NO hesitation taking out a 100# male dog that's got terrible leash manners, straight from a shelter, on a prong collar. I'm in control of that dog. I've seen those big, strong dogs pull large male shelter workers all over the shelter in slip leads (cloth choke collars). Those dogs don't do it with me, though. The difference is the tool, knowing how to use the tool, and starting the conversation with the dog before they start pulling.
Some dogs should not be in either a prong or a choke chain. They're soft, submissive, fearful, etc. -- I'd rather they be trained in flat collars, or at most a martingale collar. You have to know your dog. I also prefer working with a trainer that knows the difference and isn't a "one tool fits all" kind of trainer.