I voted "under," but I really don't know why you'd want my opinion.
Has to be consistent with the overall idea a road bike, or at least as much as possible. While neither could be true "roadie" (hence here in commuting forum), I really couldn't tell which to prefer aesthetically. I honestly used the poll to decide.
I have a Vaude handlebar bag (more of a box, really) that attaches with one of those Rixen-Kaul click-fix mounts. The mount is excellent, very secure, etc; but it holds the bag higher than I like. It stands a few inches proud of the handlebar, and I'd prefer if it didn't.