I agree. Also what we see in BvS is a Batman that is first lost and is simply on the wrong path (as you describe), but during that story he is found again and comes back to his old ways; he last line is: “I failed him in life, I shall not fail him in death”.... in other words, he is in the end not a killing vigilanty anymore and this perhaps answers the OP.
Also obvious in his rescue of Ma Kent. Here his fighting is perhaps very brutal, but not lethal - at least in intention. He disarms them first, destroys their weapons etc. His fighting style and approach is visibly different from his approach in the beginning of this film. The scene where he shoots the gas tank to save Ma Kent is directly lifted from Millers comics. Except in Millers version, Batman headshots the bad guy... the fact this scene deviates so fundamentally on only this is to show us (I speculate) that he had changed his old evil ways...
A bigger answer; Cavill's Superman does not kill because of his experience with Zod. The remorse and pain he experienced here taught him his place in the world. He is no executioner, he is a servant of justice (and beside, ripping of Lex's head would have solved nothing and possibly indirectly killed his mum)
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