How different would the game be? and what would you think Bungie could add that 343 didn't?
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If Bungie did make Halo 4, I would imagine that instead of Spartan Ops, we would have an evolution of FireFight. In addition, Customs, Forge, community features would probably feel more proper and finished. On the negative side of things: I don't think Bungie could have done what 343 did with Halo 4's tech - the game is gorgeous for an Xbox 360 game. Also, I don't think the OST or gameplay would have been any better with Bungie at the helm (on the account that that was where Bungie was heading, as indicative by Reach).