In the latest move to current gen platforms, Bioware is limiting the latest batch of DLC to Current Gen consoles only.
The last batch of DLC, Jaws of Hakkon, came first to the PC and Xbox One back in March, only later moving to PS3/PS4/Xbox 360 in May.
According to Eurogamer, a post on Dragon Age's official website details a save importer functionality, carrying over items and files from older consoles to the newer one. The key line looming in that report?
"All future Dragon Age: Inquisition DLC will be available on PC, PlayStation 4, and Xbox One only..." 
 - Eurogamer - Dragon Age: Inquisition to ditch PS3, Xbox 360, for future DLC - http://www.eurogamer.net/articles/2015-07-07-dragon-age-inquisition-to-ditch-ps3-xbox-360-for-future-dlc