@neil To me the "function" here is ability to communicate privately with someone you've interacted with on the site in question. The rest is a matter of UX and privacy properties.
Integrated "DMs" might have slightly better UX; that could be improved a lot if OOB private chat systems had better invite link support.
The privacy properties are where things get really different. The reason I strongly dislike integrated DMs is that the social contract about privacy ("they're private") is grossly mismatched with real capabilities a BOFH might exercise or that the state may force the operator to exercise.
OTOH OOB links like I proposed have a tendency to leak links between identities, especially since most of these platforms don't let you use private per-interaction subidentities.