Here's the rundown:
Right now, Dianamon's entry is not accessible in the Field Guide, it is not possible to see Dianamon in the evolution tree, and the purple (formerly DLC) quests are missing in both the PS4 and Vita versions. The only known sighting of the DLC quests in localized form is from RespDMO's playthrough of the PS4 version, which is suspected to be a reviewer's copy as it was released prior to the game's actual release.
At the very least, Chapter 5 and 6 have a number of missing voice sections (the ones that come to mind the most are Yuuko's gloriously fake bad acting and
, but there are others). However, after comparing with the Japanese version, I haven't noticed anything missing after that. I've only encountered reports of this problem in the Vita version, although I haven't heard accounts of it not being in the PS4 version (i.e. it's possible that simply nobody who's gotten this far has reported it yet). Gameplay videos on YouTube are still rolling out, so we'll probably see in a matter of time.
There is a reported problem (serial case) in which people who bought the first-month Vita version (and got its preorder bonuses) but did not preorder the PS4 version (and therefore did not get its bonuses) are now unable to cross-save due to the DLC incompatibility.
What this means:
Although it seems the formerly DLC quests and Dianamon were fully localized, and Dianamon was shown off at a Bamco stream, there seems to be clean no sign of her or her associated DLC in any version of the game currently released commercially. It's possible that Bamco may simply want to release those as DLC later, as was done with the Japanese version (only the people who preordered were able to download it from the get-go, and everyone else had a delay). It should be noted that purple is still referred to as being "DLC" quests in the localized game, which would contradict the idea of them being on-disk. The fact it was in a review copy also strengthens the idea of it coming to the game eventually in some form.
It's possible the voice issue may just be a voice issue and nothing more than that, and if it's the only problem it's possible Bamco may not consider it a big enough problem to warrant a patch.
At the very least, though, they probably need to do something about that cross-save issue.
There is no concrete evidence that any of the content issues are Vita-exclusive, as this arose from a misconception in relation to RespDMO winning the circumstances lottery and getting a pristine copy with the full content and such. As of now, there aren't any currently known differences between the PS4 and Vita versions other than those reported prior to the game's release.
