Sure they could have written a more traditional scene where Superman stops Zod without killing him, I like the fact they they took a different route and did something unexpected. I don't see Superman's reaction to killing Zod as being hammy. I thought it was good acting and emotional.
Or Superman could have ambiguously just thrown him into a pit of mist and clouds like in Superman II.
I love that movie, but come on! That scene doesn't bother me it is just ironic that people complain that Superman kills Zod in this movie and yet it is implied that he killed him in Superman II but because it is shown in such a "G" rated manner nobody bats an eye.
I thought that scene in SM II was weird, but come on. He could have been throwing him into anything. I've always just assumed it was some kind of prison, or somehow putting the back in the negative zone. Based on the tone of the other movies, I doubt he was supposed to have been killing them.
Anyway, Superman not killing is part of the character. Pre Gritty DC reboot, He would never kill Zod. Zod could be shooting his eyes at Lois or Ma Kent and he wouldn't snap his neck. But, comic superman was also a hopeful person and had personality, so maybe its not a good compariosn. Still, its like I said. The Zod neck snap is exactly the same as if Batman had just shot Bane with a gun in TDK Rises. Its an action that is totally against everything the hero is about. You could probably find a time in the golden age where superman killed someone, or bizarre rare occurrences of idiot writers doing it in more modern times. On the same token, Batman used a guy on Darkseid in Final Crisis (it was a super science gun, and it was already established that Darkseid would survive into the 31 century so he wasn't actually killing him, but it still kind of counts).
But, its still the most anti superman thing ever. The point of superman isn't to make him super realistic (which they didn't, but they tried). He's supposed to be a hopeful guy, a guy so good that he's literally a superhuman. He doesn't kill, and he saves the day. Making him (and the movie) dark and gritty was just a weird tone that didn't fit the character, and the killing was part of that. They definately have an uphill battle to make Superman/Batman good. I'm hoping they do something with superman realizing that he was wrong, and vowing to never kill again (maybe batman can teach him that lesson). That would atleast make the death not just a pointless moment for people who think every hero should kill the villains

Otherwise it becomes a comedy sketch, with Superman just snapping every villain's neck. If he'll do it with Zod with no real hesitation (and he really didn't hesitate, he didn't even try to move Zod or stop him, he just yelled at Zod few times) he has absolutely no reason to not snap everyone's neck. If he can justify Zod, he can easily justify killing any bad guy he comes across, from muggers to supervillains