This is a great question.
Short answer: No, the evidence does not suggest that positive reinforcement is universally more effective than negative reinforcement or punishment. However, there are still good reasons to focus on rewards over punishment in real-life training/learning situations.
The trouble for folk psychology began with Skinner's somewhat unfortunate choice of terminology... While Skinner advocated positive reinforcement over negative reinforcement or punishment, it seems to have remained an industry secret that what he meant by those terms is not what the general public thinks he meant.
The modern view of positive and negative reinforcement is that they are essentially synonyms. They are different ways of looking at the same thing, like describing a glass of water based on how full or how empty it is. Computationally, as you say, learning algorithms that assign positive values to targets or negative values to non-targets are mathematically equivalent.
Although they are often confused with positive and negative reinforcement, rewards and aversives are different terms with different meanings. Testing whether one is more effective than the other is tricky, as in practice they are usually qualitatively different. For example, is ice cream or spanking more effective for getting your kid to do their homework? The answer is: It depends - how much ice cream, how much spanking...? Surely we can find a ratio of ice cream to spanking at which they are equally effective. The type of research that examines this question is interested in determining where that boundary is (here is an example). Thought experiment: How can qualitatively different feedback mechanisms be applied in machine learning?
Research more likely to answer your question compares positive and negative feedback that is arguably qualitatively equivalent. For example, compare gaining money to avoiding loss of money, reducing risk to avoiding increase in risk, and it's even possible to compare the effects on animals that are trained in a token economy. In recent years, the folk psychology idea that positive feedback is universally superior to negative feedback has been called into question by such research. A few examples:
Neurological reasons for the difference in effectiveness between positive and negative feedback have been proposed - for example by Eveline Crone in the study cited above.
Training using rewards is preferred for animal trainers, parents, and teachers in most practical situations:
- There is usually a much wider range of undesirable behaviour to punish than desirable behaviour to reward. Animals and young children have difficulty determining what the desirable behaviour is with only clues about what behaviours are undesirable. Adults are easier to work with because you can explain the desirable behaviour in words.
- Punishment must be applied to all undesirable behaviour to be effective, while reward need only be applied to desirable behaviour, and even then only intermittently, to be effective.
- Due to classical conditioning, subjects may attribute punishment to factors unrelated to their behaviour, such as the trainer or the classroom. They may learn to avoid the trainer, or avoid getting caught, rather than the desirable behaviour.
- Notice how none of these points apply to machine learning, where the process is structured, constrained, and automated.
John Maag summarizes reasons to promote positive reinforcement in schools: Namely that teachers often find it convenient and effective (in the short-term) to administer punishment and are overly reliant on it in many situations where positive reinforcement would be more effective and desirable.
Nice video on the topic.