The Reason why I think Halo 4 is going to on the next consoles is based on logic, and hints of product directions.
My main Reason is the technical side of it,
Halo is not just an Epic Exclusive Franchise to microsoft, Like other Xbox exclusives, It demonstrates the capabilities of the console its running on, this applies to both consumers and other developers showing them what they’re product is capable of running.
Now the Reason why I think Halo 4 will be on te next console based on this logic is the fact that I think they have squeezed everydrop out of the 360 with the Reach engine ( Even pushed it too far at times with some framerate issues in some parts ) so it would not make sence to start a Fresh new trilogy with a fresh new company using the 360 since it has pretty much peaked at what it has to offer.
Now the other reason is when I saw an advertisement on the 360 dashboard where if you trade in your Xbox 360 Elite against a brand new full spec Xbox 360 slim at GAME it will only cost you £100 ( £99.99 ) now this is a very cheap price, granted it is an old console but still a brand new full spec slim in basically double figures.
Now weeks before this years E3 The Wii was dropped to £100, and at E3 as we all know, they revealed there new console.
So it would logically make sence in a business term to Launch a Brand new trilogy on the brand new console.
Thoughts?
EDIT:
Wouldn’t it be great if they would put up the Halo 2 Servers once a year on the Release date of Halo 2 back in 2004 just for a day.
Reach was pushed to the limitations of that engine I believe. But an upgraded engine could come to fruition. But I do believe that Halo 5 and 6 will be on the next console.
Halo 4 will be released in 2012. The new xbox will be released sometime in 2016. There’s no way in hell 343i is going to delay the game for 4 years simply because of the new console.
When Halo 4 was revealed, it was after the point where the MS representative said “Everything you see from here on out will be on Xbox 360”
> Halo 4 will be released in 2012. The new xbox will be released sometime in 2016. There’s no way in hell 343i is going to delay the game for 4 years simply because of the new console.
The 360 is at the end of it’s life span as it is now in 2011.
Halo 4 in 2012 new xbox in 2013. Before you say that won’t happen remember Halo 2 (2004) xbox 360 (2005)
If that’s the case then Halo 4 still won’t be able to get on the new xbox console. It’s still a year away from the release of the new xbox.
But hopefully we can play Halo 4 on the new xbox then 
I agree with the OP. It would be better on a new System.
But this is kindy interesting:
> Fun E3 fact: It took Phil Spencer three seconds to answer “yes” when asked if Halo 4 was coming to Xbox 360. Read into it what you will.
It would be great if Halo 4 is really only coming out on new system as a launch title. Holiday 2012 Release for the Xbox sounds right to me
Well guys the Xbox came out in 2000 then came the Xbox 360 5 years later we are now 6 years after the 360 was launched, 7 years later them declaring a new console isn’t too outrageous no?
Oh and the guy who said the new Console is coming in 2016? I think you mis understood the meaning of a "10 year Cycle ", A ten Year Cycle only means that they will support that console for ten years not wait ten years then release the next console Hence the Xbox being released in 2000 then the online services being cut on April 15th 2010 ( No Halo 2 
).
Besides Imagine if we were sat here still playing the original Xbox waiting for the new 360 to come out? not very realistic.