The only account that you will have your beta emblem on is the one you participated in the beta with. Since you played on Xbox 360, you can use your beta rewards on Xbox 360 and/or Xbox One (as long as you're on the same XBL account).
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Edited by Rept: 8/23/2014 2:46:36 AMSon of a-. Well thanks for answering you... I assume Mentor means you're in a position to know this stuff... Are you Bungie?!
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Shhh....he doesn't like people knowing his secret identity.