A simpler way to say "more semantically correct" is "correct." Please don't trivialize the importance of semantics. Proper semantic representation makes documents more accessible.
I don't find the header, article, section, etc tags to be sufficiently clear that they are always used in the same way by different people. But maybe I'm missing something -- how do they improve accessibility?
Take a look at http://accessiblehtmlheadings.com/ for a pretty solid introduction. The tl;dr: is that, used properly, they enable screen readers and similar to identify document structure and make it more easily navigable.