As far as I understand it your achievements would carry over, but not your saves or DLC.
QuoteGames, gamesaves, and apps: Xbox One is not backwards-compatible with your existing Xbox 360 games, gamesaves, or apps.
http://support.xbox.com/en-US/xbox-one/system/move-from-xbox-360-to-xbox-oneI guess a question to you (and to anyone else with the 360 version). How does the game hold up on Xbox 360. Was thinking of picking this up for a friend, but was wondering if I should just wait until he upgrades to the new consoles. From what I've seen the visuals look pretty good, but I've heard the load times are not that great.