Don't Install 'Doom 3' on 360... Period

The main reason you shouldn't install Doom 3 BFG Edition on the Xbox 360 is that it may cause your XBLA game files of Doom/Doom 2 to be corrupt.

According to Bethesda, "Installing Doom BFG files to the system's hard drive could cause a conflict with the existing XBLA game files."

I say you shouldn't install the game because it's absolutely terrible. Installing it would be a waste of time, and especially money.