In the original version of Kingdom Hearts Birth by Sleep and it's reissue Kingdom Hearts Birth by Sleep Final Mix, despite original plans for the game, cutscenes with Terra's armor did not feature a cape. This was due to technical difficulties that the Osaka team encountered while developing for the PlayStation Portable.
At E3 2014, co-director of the series Tai Yasue originally announced that although they acknowledge that many fans would like to see the capes return, they would not be implementing them due to time constraints-- however, with the game now released in Japan, we now know that this is not exactly the case!
A cape has been added to Terra's lingering armor in this cutscene at the end of Kingdom Hearts Birth by Sleep Final Mix, with the release of Kingdom Hearts HD 2.5 ReMIX. This will be consistent with the Lingering Will boss fight in Kingdom Hearts II Final Mix, where the character had a cape. Unfortunately, capes are still missing during gameplay.
You can view a comparison image that shows off the new model with cape included, below.
Update: Thanks to our partner Everglow we now have a recording of the cutscene in 1080p. You can view it below.