Here's why it won't happen with Destiny: (Gaming)

by CyberKN , Oh no, Destiny 2 is bad, Monday, March 14, 2016, 16:49 (2976 days ago) @ Kermit

Testing.

If you start throwing different consoles and data at each other, the number of potential weird bugs starts multiplying exponentially, requiring many, many more man-hours of testing and QA. It's probably why we don't have cross-generation play now. No right-minded programmer wants to deal with a crash-bug that involves 2 PS4s, an Xbone, and and a 360.

I bet you're right, but Bungie has said that they're not the issue. Also, Destiny seems to operate remarkably independently of the hardware. I'm always surprised when I relogin to Destiny after a day or so break I'll hear the Cryptarch or whoever talking to me before I get a disconnect error (because that's my location and state when I last quit).

I can't find a source for that quote, but I would bet that it's in the context of character transfer, not cross-platform play.