This may come across as a mister-know-it-all answer, and I'm sorry for that, but ask yourself this: Who lets go and who controls?
If you see that there is no one letting go and no one controlling, you see that both instructions are wrong in a sense. They split the experience up between "you" and "the mind". The instructions "you let go" or "you control" are thus both incorrect. Of course, the teachers have to say it like this, because when putting things into words, you need a framework. If you can see behind this veil, by having some experience in meditation, you see you don't always know if it's letting go or controlling that happens in meditation. Take anger for example. Option one: Anger arises, if it is let go it go, it is replaced by kindness. Or option two: Anger arises, it is replaced by kindness, so it is let go. Who's to say what's what? It's not always so clear.
On the more conventional level, in my experience, usually when mindfulness is weak (so the hindrances are strong) it is useful to deliberately replace states of mind. This is at the level of course thoughts still. When mindfulness is stronger and thoughts are disappearing, it's better to not take deliberate action, because it will create too much restlessness. So the 'let go' instruction can be seen as a tool mainly for restlessness. Although in the end, it's all about letting go in a sense.
The Buddha instructed both ways. He said whoever makes letting go their object easily achieves samadhi. But he also gave more "taking control" instructions. Even thing like "crushing the mind". So he also said we should learn to be skillful enough to see how we should treat the mind. Sometimes we relate to it in one way, sometimes in another way.
At a certain point in meditation everything goes automatically and you forget about the instructions. But I dare to say that it is one of the most common problem preventing people from deep meditation: they don't stop interfering with the mind. So that's why Ajahn Brahm gives it so much importance.
I can't speak for the teachers, so this is only my view. They may agree or disagree. I know Ajahn Brahm also teaches some deliberate actions in the first stages of meditation. Don't know too much about Ajahn Sona.