360 and xbox one cannot play together. However, if you start on 360 and upgrade to xbox one, you can transfer your characters to the next gen if you keep the same gamertag.
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I cannot do that :/ my brother plays on the Xbox 360 and I play on the Xbox One. And it is possible but Bungie thinks people will complain about the graphics being an "advantage" for new gen, which I don't get at all.