UNTAGGED SPOILERS IN THIS POST
The difference is that Jack is the true monster of Rapture and his transformation into savior is his arc. Jack was built by scientists to kill that was perfectly adapted to his environment. He splices constantly, loading up with far more plasmids and tonics than even the most vicious splicers he faces against. The Would You Kindly Twist is the mirror into the face of the player where you're supposed to realize this. You are the king splicer. You are a killing machine built by scientists to do their dirty work.
I don't think I really agree with this thesis. Someone is not a monster because of their environment and how they were molded. Someone becomes a monster or an angel because of the choices he or she makes when left to their own free will. (see: Frankenstein) Jack/player is dropped into a world with a very strict set of rules – kill or be killed. It's Lord of the Flies.
The choices that make one a monster in that world are simple – kill the weak and the innocent. But Irrational doesn't seem to care much about the innocent, actually. The weak (Little Sisters), yes. Protect them or be branded a Monster. But the innocent Big Daddies? Irrational says, these are expendable creatures.
And that's the central problem – you have no choice. It's an illusion. Oh yes, the Little Sisters, yes. Kill them or don't. But in the case of the Big Daddies, the game ceases to narrate based on player agency and instead becomes a linear interactive fiction. Once Irrational says, "No, forget about your choices, we're going to tell you what to think and how to act!" because they're too focused on funneling you through to the end of their moralistic tale, then it ceases to be a game. And even more damning, it ceases to be provocative.
One of the most obvious perceptions the player and Jack makes is that Big Daddies are monsters. There are audio diaries on how they are monsters, the supporting characters call them monsters, and they definitely look and behave to meet your expectations as monsters.
I never had that perception. I quickly realized that Big Daddies were one of the few characters in the game who wasn't a monster. They never went out of their way to attack me. They protected the weak. Which is why I never wanted to kill one, and found it painful to do so and made me angry at the game for forcing a decision out-of-step with the established morality system of protecting Little Sisters. Sure, many of the citizens of Rapture felt the BDs were monsters, but the real monster was the unchecked libertarianism of the society. But they couldn't even see they themselves were also monsters, since they participated and profited from the system which created the BDs.
Killing Big Daddies is supposed to be sad, not immoral like it is Little Sisters. You have to kill them to save Little Sisters and to save yourself, but killing them is killing the only selfless beast in a city of individual extremism. By becoming one you are inverting your character roll in the game. You go from a splicer on a mission to kill to a Big Daddy on a rescue mission.
Supposed to be sad, not immoral? That attitude is equivalently "the end justifies the means" as the rampant gene experimentation which destroyed Rapture. Killing one Big Daddy to save yourself and the Little Sisters may be the blessed moral decree of the game, but it is flawed logic. If killing a Little Sister is evil because they are weak and innocent, then killing an innocent Big Daddy should be equally evil because they are also innocent. It's no different than saying, "we had to bomb someone else's civilians to save our own civilians." Taking a life is still taking a life.
At the very least, the game should have presented this as a weighty choice and allowed an alternate path, and not simply a mandatory checkbox on a mission screen. Or, if Irrational didn't really care to discuss what makes a wo/man into a monster and free will, then there should have been no consequence for killing a Little Sister. The problem is Irrational tried to dabble in both free will and societal responsibilities, but ended up with a bit of a narrative and thematic mess.