Battlefield 4 has a mandatory 2GB install on Xbox 360, and over 12GB of additional installations should you wish to use them. DICE recommends doing them, however.
In an update posted on the EA Blog, DICE confirmed the mandatory 2GB install and added that Battlefield 4's first disc houses the multiplayer, and offers an optional 6.6 GB of content, while the second campaign disc holds 5.8 GB of content.
You can choose to run these off the disc, but the blog continues, "We highly recommend performing these additional installations to make sure you have the best experience possible in Battlefield 4."
Better start clearing your hard drive space if you want the best experience folks.