Replace your first word with "Reward" and re-read it.
My own observation is that both of these claims are partly true but that there is some effect that remains even when they think they are not observed. Parents often see what kids think they don't, so I have empirical evidence of this (as all parents do).
I don't buy the idea that punishment and reward are just different sides of the same coin.
Reward works well for building a healthy rapport and relationship. I don't think punishment is entirely ineffective, but if it isn't rare and judicious it may well end up causing more harm than help. The problem is that the response to punishment is visible immediately while the downsides may only appear many years later.
Rewarding someone when they do what you want is just as sleazy and manipulative as punishing them when they do what you don't want. It might be the fact that a child doesn't realize that, but an adult undoubtedly (eventually) would, and be just as resentful.
Similar to what I've been reading about in a book about democracy. Rules that are regarded as legitimate barely require enforcement, people will follow them of their own volition. Rules that don't have legitimacy are actively resisted.
Is that your goal?