The Ultimate Edition comes with
The Latest Patch, which is huge because it makes the game very playable. 65 hours in with the Ultimate Edition on 360, no freezes and only issues I have are typical Gamebryo issues.
Dead Money, Honest Hearts, Old World Blues, Lonesome Road, Gun Runners Arsenal and Courier's Stash. In addition to New Vegas.
It's worth getting.
HOWEVER. if X-Box is like the PC and uses Steam, then you are going to NEED an internet connection to activate it. But once it's activated then you can play offline no problem. Maybe someone with X-Box can confirm this requirement.
No internet requirement is necessary for 360, just put the 2nd disk in, install, and then afterwards play the 1st disk.