They shouldn't. Store codes typically refer to a specific online store item that is coded for a certain console, which is why you cannot transfer the DLC (aside from Activision controlling the distribution of content). Whilst it would be great, the two stores (Xbox 360 and One) are separate in all ways but name and managing entity, so chances are they require codes that were originally meant for their specific version of the store.
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Ok, thanks for helping me out
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Thanks guys, just spent aaaages looking for this info as I realised that I can buy a new physical version of destiny on 360 (which comes with codes for all 3 DLCs) for about $30-40 cheaper than the Xbox store's download of TTK, so I was hoping that both stores might use the same codes (and it would have the advantage of also giving me destiny on 360 in case for some reason I ever wanted to play on lastgen) and I could save some money (70 AUD is waaaaay too much to ever pay for any expansion). Still cheaper to buy a new copy for xbone than buy the dlc on its own, so meh. Only saving $20 now instead of $30.
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Of course.