production - What comes first, the music or the take?

As a filmmaker, I can provide some insight into this, however there are always going to be exceptions to the rule.

In general, a film is scored after editing—a notable exception to this would be the specific use of a particular piece of established music, in which case the editor may well be asked to edit to the beats of that music.

For a scored film, it is important to get the edited film to a 'lock', which means the visual elements (SFX finished or not) are in place and edited. There is a sense of visual 'timing' that an editor can employ, and this might well affect the composer's decisions.

Once the picture is locked, the composer can then go in and create the music, whether it be sweeping themes, leitmotifs, or short snippets to emphasize a scene.

In order to stay on budget, the producers do not want the composer having to rework pieces to fit re-edited sections, which is why the picture lock is so important.

(I'll add more to this answer in a few hours: on the road right now ;)