I don't use choke collars anymore because that thin chain is more like a 'choke' , like using a piece of rope..Thats' why they call them choke collars
Martingales tend to be a wider type of material, some with a chain at one part of the collar, sometimes it's material..since it's wider, I don't feel they 'choke' as much if at all.
I get my martingales from the vendor here The Ultimate Leash, met him at a horse expo, love his collars.
Prongs are self correcting, that 'pinch', pinches, get the dogs attention quicker, so they stop in their tracks, no pulling.
Unless your 'hanging' the dog they are not going to stop breathing..A choke can cause trachea damage I believe. I would think it all has alot to do with the handler's training ability as well.
I have used all three, choke when I was doing competition obedience not because of the corrections, because it was a sleeker look at the time. Prongs I've used on dogs that I felt I needed it when training, and then phased out.
Martingales I use now on Masi, not for the 'choke' aspect, but because I like the collars and if I want to issue a correction I can, tho she walks really well on a leash and doesn't pull.
Just my opinions