Last gen and next gen games are not compatible with one another. Purchasing a game on one platform does not grant that game on other platforms, unless a special offer exists. Destiny does have a special offer that allows last gen purchases of Expansions I and II to upgrade to next gen at no cost. The offer does not, however, apply to The Taken King. Therefore TTK must be separately purchased for each platform on which you wish to play it. https://www.bungie.net/en/Help/Article/12122