I always thought Bungie used an in house engine called Blam!
So with that assumption it's probably the same engine they used on Reach which in turn is from the previous Halo games.
English
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Nonononono, I am the Blam! engine. IYKWIM
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It won't be the Reach engine. Judging by the amount of time they've been working on Destiny, it'll likely be a very unrecognisable version of either the Reach engine or possibly something largely new, with current/updated engine code plugged in. A reminder that the engine most certainly does not make the game.