The only way digital 360 version will work on One is when it's made available for BC. Your character can be played on either version of the game, but at the moment, each game is console specific.
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Edited by MyGuitarTSP: 9/18/2015 2:45:20 PMNo. If you bought Destiny for the 360, you were able to download it for free on the Xbox One. It goes for both Expansion Packs too.
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Ah, I stand corrected. Only have on One, and definitely didn't go the other way.