This is a bit old, but it's probably worth mentioning, since it will affect the 'hackability' of the next Xbox. Windows For Devices has speculated on the nature of the operating system behind the Xbox 360. Their source claims that the 360's OS is a highly modified form of the original Xbox OS which, in turn, is a highly modified form of Windows 2000. The importance of a stable and intuitive operating system is much higher with this generation of consoles and especially in the 360, given the immense focus on the device as a media center and communications system. Instead of simply maintaining enough firmware to run whatever game is plugged into the machine, the 360 will maintain your media library, interact with other devices and more. Either way, they unequivocally rule out Linux as the 360's OS (but that doesn't mean someone else couldn't figure out how to install it post-purchase).
The Xbox 360's Embedded OS [WindowsForDevices]