As far as I know -- I admit I don't know a lot -- the studies you want haven't been done. There have been studies comparing reinforcement, punishment, and a combination of the two, but the studies didn't break reinforcement and punishment into positive and negative. (No, I don't have cites for those.)
I think however, the question is flawed. The definitions of R+, R-, P+, and P- are based on results. They say behavior increased or decreased. They don't say "a little bit," "a lot," "permanently," or "until something better comes along." All five parts of OC (including extinction) *work* by definition. Within reinforcement and punishment, every application -- positive and negative -- falls on a continuum from mild to severe, depending on the situation. Neither positive nor negative is innately "stronger" than the other.
So what you're asking about is reliability. Reliability is a number, pure and simple. One type of punishment or one type of reinforcement is not, by definition, more reliable than another. Reliability comes from application, from repetition, from a good solid training plan, and from a dedicated trainer.
The Baileys did not publish, as far as I know. However, in the nearly 50 years (15,000+ animals in nearly 150 species) that Animal Behavior Enterprises operated, the Brelands (and later the Baileys), who were scientists first, kept exhaustive records on each animal.
Though they were leaders in the push for humane treatment of animals, they were not guided by moral choices. They chose these methods because they gave them the results they needed in a timely manner. They chose them because they worked.
Many of those animals were for those "automated" exhibits they used to have at fairs -- "play tic tac toe against the chicken," for example. They also trained some pretty elaborate all-animal stage shows. However, not all of their work was commercial. Much of it was for the government. Beginning with the "pigeon-bombing project" of WWII through most of the Cold War, they had lots of interesting training challenges.
Distance work was a given. Wild-caught birds free flew for hours in a hundred-square-miles. Wild-caught dolphins swam -- alone -- four hours away from the boat. The cats were guided from great distances by sound.
Whether the project was commercial or for the government, the Baileys required reliability. Not kind of reliable. Not even most-of-the-time reliable. Reliable. They weren't going for scores or a ribbon. There were, in many cases quite literally, human lives relying on the reliability of these animals' behavior.
And the method they used was the same one we're using here. They used positive reinforcement, extinction, and occasional negative punishment. They used positive punishment only about a dozen times in 50 years and 15000 animals -- and those times were at the request of the client.
They didn't choose this method because it felt good. They chose it because it gave them the results they needed in the fastest time. They experimented to find the best way. Trial and error. But most importantly, they kept DATA -- gobs and gobs of scientific data -- and based their programs off of that. What they "felt" like they knew simply had no bearing. Only the numbers, only the results.
The method -- the same method we're using here today -- is the method they found worked best. And it worked for every individual in every species they trained. That, more than anything else, convinces me to stick with this training method.
Honestly, the whole argument is utterly irrelevant. The Baileys have proven it can be done. Period. What remains is whether an individual trainer is capable of doing it. I've seen reliable traditionally-trained dogs and unreliable ones. Reliable positively-trained dogs and unreliable ones. Good traditional trainers and poor ones. Good positive trainers and poor ones.
If they're interested, they'll check it out. If not, their minds are closed, and they won't listen to anything you say. Don't waste your breath. Just train your dog to a level of reliability that satisfies you.
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