Right now neither disc can be installed for some reason. A lot of people are unhappy about that.
The game seems to be split between the two discs. The intro is on the first disc but before you head to the Sarif Manufacturing Plant you are prompted to switch to disc 2.
Content from Missing Link is also on the first disc as well and continues on chronologically (i.e. DLC actually plays where it is supposed to be as part of the core game, unlike the "stand-alone" nature from the original version).