tl;dr: Vote to close with the reason that you think applies the best. If you're optimistic, you can also comment to explain your vote and explain the best way how to improve the question in your opinion.
The question will actually get closed as quickly no matter what reason you choose. Indeed, a question gets closed as soon as it gathers five votes to close, all the reasons combined; the reason with the majority of votes will be displayed, so for example a question with 2 votes to close as off-topic and 3 votes to close as too broad will get immediately closed, and the reason displayed will be "too broad". (See here for more info.)
It doesn't matter if other people think another reason applies. Often a question that deserves to be closed is flawed in several ways, but there's often no real argument as to whether the question should stay open. The end state is the same no matter the reasons chosen: the question is closed (well, "put on hold" first), cannot receive new answers, and becomes eligible for (possibly automatic) deletion after some time.
In general it's preferable that a question that needs to be closed gets closed for the correct reason, but if it gets closed for the wrong reason I don't think it's that big of a deal. The main concern is that the OP gets correct information on how to best improve their question to get it reopened, and you can simply use comments for that if you think the reason used was not the best one. I don't think reopening and reclosing a question simply for the sake of changing the reason displayed is a meaningful use of one's time. (I find that many users do not even read the reason displayed, for some reason. Apparently on mobile the reason is not very prominent.)
So to answer the question in the title: No, it's not very important.