I`ve recently upgraded to a One X from a 360 and you can still do a D1 character and content migration.
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I would assume that is because you had characters on the legacy version of Destiny and Bungie migrated the data to the XB1 servers. You definitely cannot migrate data if you have started characters since the start of August as we started Destiny 2 with new characters last night and there was no way to carry over a previous character.