UPDATE: Activision has followed up and confirmed what was orginally announced still stands: individual DLC packs will transfer on PlayStation.

Additionally, for fans looking forward to the Call of Duty: Ghosts Onslaught DLC Pack, please note the following with regard to transferring DLC from Xbox 360 to Xbox One. If you are a Call of Duty: Ghosts DLC Season Pass holder, then your Onslaught DLC Pack will carry over from Xbox 360 to Xbox One. However, if you are not a Call of Duty Ghosts DLC Season Pass holder and purchase the Onslaught DLC Pack individually, it will not carry over from Xbox 360 to Xbox One. Currently, Microsoft only supports DLC transfer between Xbox 360 and Xbox One if you are a Season Pass holder. The Call of Duty: Ghosts Onslaught DLC Pack will carry over from PlayStation®3 to PlayStation®4 whether you purchase it individually or get it as part of the Call of Duty: Ghosts DLC Season Pass.

Activision has posted a new support document updating the rules regarding DLC transfer for Call of Duty: Ghosts.

Notable changes include that DLC now only transfers from Last-Gen to Current Gen, meaning Xbox 360 -> Xbox One and PS3 -> PS4 only. It will not transfer backwards.

For DLC packs, now, only Season Pass content transfers. Individually bought DLC packs will no longer transfer on any platform.

Call of Duty: Ghosts DLC map packs are available in two ways:
-With the Call of Duty: Ghosts Season Pass, each DLC pack is pre-purchased and will be available to download on the day each pack is released.
-Each DLC map pack can be purchased individually though the in-game store, or through the Xbox Store or the PlayStation Store.
-If you plan on playing the DLC map packs on more than one console generation (i.e. both Xbox 360 and Xbox One), please refer to the following guide:
-Content only transfers from the previous generation to current generation (Xbox 360 → Xbox One, PS3 → PS4). Content will not transfer backwards.
-The only content that will transfer are map packs acquired though a Season Pass purchase. Individual map packs purchased individually do not transfer.
-Customization Items do not transfer, including:
Personalization Packs
Legend Packs
Special Characters
Extra Slots Packs
The Wolf

SOURCE: Activision Support via @xMaccabix