I can see how this would work out. As Locke and Chief meet and talk, they might have to work together against Forerunners, because, don't forget, there is another mysterious force at work here, and Covenant Remnant. After exerting maximum effort, and blasting through their ammo they finally clear the area after both retreating to the location (Possibly the one that they're at now.) , where Locke or Chief, turn on the other, leading to the scenes shown in the trailers shown in the OP.
In Locke's trailer, in my opinion, he sounds frustrated with how much effort he must've put in to follow Chief's trail, which could be an explanation as to why he threw his weapon to the mud below.
In Chief's trailer, John sounds, imo don't flame me, completely changed, maybe it's his voice actor or intended but the ability to spot whether Chief is speaking to Locke, Himself, or even the "Monument" is eerily hard to choose.