Good research.
Let’s call the left diagrams the conjunction or non-nested model. The right is the modifier or nested model.
It’s good to learn both but also to have a general policy for what to use (don’t try to make it up in each individual case – only switch from your default if there’s a major reason).
I strongly prefer the conjunction model for coordinating conjunctions. I prefer the conjunction model for subordinating conjunctions because clauses are significantly bigger and more important than typical modifiers like “the”, “red” or “very”. I prefer the modifier model for relative pronoun clauses like “I met Sam who is tall.” because the primary purpose of those clauses is to modify a noun. The relationship where “who is tall” is a modifier for “Sam” is clearer than calling “because clauses are significantly bigger and more important than typical modifiers like “the”, “red” or “very”” a modifier on “prefer”. The conjunction model actually works poorly for relative pronouns (it results in trees you probably won’t like), but it works OK for subordinating conjunctions (it does get messy when there are many clauses, but the main issue there is that sentences with many clauses are messy).