When determining if the best action is to down vote or close, I think the best thing to do is to take cues from the hints on the site.
Closing, as Pat points out, doesn't kill a question, it prevents people from posting answers until it's cleaned up. Voting to close a question brings up a dialog box prompting you to select one of five reasons why the question should be closed. If it doesn't meet one of those reasons, then closure probably isn't the right answer. The whole point is that the closed question is put in time out until the problem is resolved, at which point it can be re-opened--or deleted if no one cares enough to fix the problem. I've seen questions get closed, fixed, and re-opened.
As for down voting, it really has a different purpose. Closure indicates a structural flaw in the question: it's an exact duplicate, it doesn't have an answer, it belongs on another SE site, etc. Down voting serves to suppress a question that doesn't meet the criteria for closure (i.e. there's nothing structurally wrong with it), but just isn't well asked.
Jeff points out a good criteria as he explains why the down vote hint has changed: a good question is not only useful but reflects a little bit of work on the part of the questioner. Now this isn't a coding site, so the idea of research is likely to be a little different, but I always cringe when I see someone ask a question that is answered by quoting a crystal clear sentence from the rules.
Take a strawman question like "How many dice do you roll in Monopoly to figure out how many spaces to move?" It's a board game question, so on topic; it's objective, a real question, not a duplicate, and not too localized. But, it's boring and lame an has an easy answer (and isn't even worded very well). I'd down vote that because the question is disrespectful of the time that another person might take to answer it.