As Xenos said, bungie has a check load of data on their site that they can do whatever the heck they want to with it. I'm assuming that if your account is linked, then yes.

[url=http://www.ign.com/articles/2013/05/23/destiny-could-get-pc-version-cross-platform-saves]Here[/url] is Bungie's official word on it so far. [quote]For us, [platforms] are purely agnostic,” [Eric Osbourne] said. “Any data on our back-end servers and services, like Bungie.net, are ours. We control it, we can do a bunch of fun stuff on that side. So for us, we want to absolutely do the right things for players. But there are some complexities we have to solve that are outside our control. But we’re absolutely pushing to solve some of those things. We don’t have anything to announce, but hopefully in the future we will.[/quote]

If you save to the cloud you should be able to retrieve it on the new Xbox

I think you might be able to cause they said your whole profile like your xboxlive account moves to the Xbox one so why not your game? Ya know? But that's only my thought