Matt Grandstaf from Bethesda confirmed that to NowGamer:
There is no performance advantage to installing the game to your hard drive.
Additionally if you still go ahead and install the game then you won’t be able to access the two classic Doom titles.
If you choose to install the game to the Xbox 360 hard drive, you will not be able to launch Doom or Doom 2.
So it’s just better off reading the game from the disc. Doom 3 BFG Edition is a remastered version of Doom 3 that includes the Resurrection of Evil add-on pack and seven new levels in The Lost Mission. Finally as mentioned above, players will also get the original Doom and Doom 2 titles.
There is still no news on DOOM 4.