There are pros/cons for both.
I believe MS want Halo 4 this gen because they are not going to invest in much new IP at this point and need another iteration of core titles, to allow 343 to release a Halo title to a large install base which gives them the best chance of success, and as because this gen is clearly lasting longer and they need tail ends boosts for 360 to cross with the release of their next console. Finally releasing Halo 4 on 360 means investing the fanbase in the new story and increasing the odds they'll buy into a new console more quickly to get Halo 5 and the next step in the new story trilogy.
The main (possible) downside to releasing Halo 4 on 360 I see is that if for some reason it is deemed not as good as Bungie led releases (probably a slim chance but one that's there) then of course the franchise could be diluted ahead of the next console, weakening the draw if fans feel the series may be about to decline. I doubt this will happen but it's a risk that exists.
The upsides of releasing Halo 4 on the next console are fairly obvious as they are variations of the above - lure players over to the new console, have a new trilogy kick off on the new console, and of course push the graphics/engine further than the 360 could support.
The downsides though are that the first 343 title will launch to an initially smaller install base and if the reception for the game was that it wasn't as good as Bungie's efforts it could harm the initial ramp up of install base for the new console. Unless MS find other IP to invest in no Halo 4 on 360 runs the risk of the console having a fairly weak tail life.
So I think overall it makes sense to launch Halo 4 on 360. The install base is there, it will help the tail end of the 360, it will set up Halo 5 for a big launch on the next console and it will stave off cries of "no exclusives" in the market better than a bunch of new, untested IP that might fail to find favour with the install base.
Try to be reasonable... its easier than you think...
