No you can't get a free copy on the 360. It only works going from last gen to next gen consoles. Also you have to buy it digitally on the 360 in order to get if free digitally on the Xbox One.
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Thanks Venom MDK for the information. It would have been nice to have this information from Bungie before buying the XBOX One version. Last time I support a company by pre-ordering. Not worth it any more if these are the tactics that they will employ to get our money. Better off waiting for the games to come down in price after they've lost the "new" factor or to buy it used. Most games are not worth the full price tag and Destiny certainly wasn't worth pre-ordering just to get a couple of days in the beta environment.