There's a new Dropbox update (v2.4.5) rolling out with the option to save files to your SD card in addition to the internal storage. It's hard to believe that's not supported already, but we checked and sure enough, you can only export files to the internal storage. That changes in the new version, along with a few smaller tweaks.
It appears Dropbox is finally getting in-line with the updated Android file management interface, which is a relief. The janky UI the app previously used was quite unpleasant. It's still a little awkward to get to the export dialog via the action button on each file, but your SD card should be listed in the location menu. Keep in mind other apps will have limited access to SD card files on KitKat because of the permission changes.
In addition to SD card exports, you also get faster searches and improved Android L support. That doesn't do you much good at the moment, but at least Dropbox is ready for the future. Now how about a UI overhaul, guys? The update will be live in the Play Store soon, but participants in the early update program are getting the new version right now.