Halo 3 is the game and only the game.
Halo 3: Limited Edition comes with an extra disc, which features a making-of, special edition gamepics and themes, and more.
Halo 3: Legendary Edition comes with the same disc as the Limited, and another which contains all the cutscenes from Halo: Combat Evolved and Halo 2, a re-made version of Red V.S Blue: Episode One, and a limited edition Master Chief helmet replica, Game case (holds four), and stand.
Rock Band is good if you plan to be playing with up to 3 people (in person or over X-Box Live), and pretty good by yourself (if you enjoy Guitar Hero by yourself), and is incredibly addicting. A great game, but only if you enjoy rhythm games.
Halo 3 is very well made and good, however if you like first-person shooters, buy Half-Life 2: The Orange Box. It's online hame (Team Fortress 2) is way better than Halo 3, but lacks in a good plot if you haven't played Half-Life 1.
All-in-all, my cup of tea is Rock Band, but Halo is more in depth and better online with a bit wider idea in gameplay, compared to Rock Band.