"The Korean children are not playing by these trees, but by those."
Translation:A koreai gyerekek nem ezeknél a fáknál játszanak, hanem azoknál.
In the case of a tree, I would say they are really interchangeable, since the tree is essentially radially symmetrical. As an example, though, if we were talking about a house, I would think something would have to be at the side of the house to be ház mellett, while it could be near the front or the back and be háznál.
There are, however, strict rules about what constitutes a neutral word order. In most cases that is the best choice. In some other cases there is an obvious focus in those cases the focus goes before the verb. In the texts you read the changing word order actually slightly changes the meaning of the sentence.
I agree that the meaning of the sentence, or at least the connotation, changes with a change in word order, but I disagree that a neutral word order is the appropriate translation of a sentence that has absolutely no context. Since it has no context, any sentence in the target language that can be a possible translation of the sentence in the source language should be acceptable.