Loglines - concept or story?

Jill asks:

I've been following your web series on screenwriting and went back through my notes on what you said regarding idea vs. concept vs. story -- very helpful by the way. I'm curious as to your thoughts on what should be written in one's logline: the concept or the story? 

 I've read so much conflicting advice regarding what to put in your logline (and seen both -- a slick, mean, six-word concept and two long sentences that describe the story/essence of the screenplay).

Ask ten different people this question and you're likely to get nearly ten different responses.  I covered this before here, where I gave this advice:

I'd say to shoot for one sentence [in length], but don't sweat it if you need two sentences to cover everything. It's also not a bad idea to include some plot details - or at least the main hook of the story and how it relates to the main character. A good trick is the TV Guide technique - write the logline the way you imagine that TV Guide would summarize the story. 

Take Die Hard for example: "A New York cop tries to save his estranged wife from terrorists who have taken an L.A. office building hostage on Christmas Eve." Bam! One sentence and I know the protagonist, the antagonist, the hooks and the stakes.

So in that case, I guess I'm advocating the concept be the logline.  But that's a helluva lot easier to do when you're dealing with a high concept idea.  What about something more character-driven?

This is the IMDB logline for Like Crazy: "A British college student falls for an American student, only to be separated from him when she's banned from the U.S. after overstaying her visa."

Concept or story?  I say "concept."  That description tells me what the film is about, but doesn't get into any of the ins and outs of the various plot turns along the way.  And you know what, that brief description still suggests enough that I can get a sense of if this is the sort of script that fits my particular needs, at least with regard to genre and scope.

But if your approach differs, please sound off in comments.