The Premium Edition comes with the 2 previous games and also Arkham Origins, not only the DLC'!
If you are a Batman fan I recommend getting the Premium Edition, it's cheaper and, as I said, it comes not only with the DLC's but also with 3 games, Arkham Asylum GOTY, Arkham City GOTY, and Arkham Origins!

It is a good adventure game with beautiful graphics, an excellent experience playing the game. You may lose hours playing the game! The bad thing about this game is that you can't change controls very well for keyboard, but if you have a command, that's not a problem.