Will my Xbox 360 downloaded content transfer to the Xbox One?

Your data for those games may** transfer over but you'll have to repurchase the games for the Xbox One.

**may doesn't mean will.

What do you mean by transfer. Destiny 360 version will not upgrade to the xbx1 version. If you want the xbx1 version you'll have to buy it.

Since the xbx1 is backward compatible you can download destiny 360 version to your xbx1 if you use the same log in.

Xbox One versions are considered different games. When it first came out they had a deal where you could upgrade to the Xbox One version of several games for $10 or so, but by now they figure if you cared you would have done it then.