Aren't you forgetting the Avengers? That featured a city wide invasion that involved aliens wrecking havoc all over New York city, both small and huge. Where as Superman fights Zod and doesn't really give a crap about the destruction that's going on around him, the Avengers are at least coordinating with each other and the city police to ensure that the civilians are out of harms way. I didn't see any footage of Captain America walking away from a gas station that was exploding just to make him look like a bada**. And even after the fight in the Avengers, we get to see people reacting to the destruction, posting photos of their missing/dead friends and families, and being thankful for what the heroes did. In the end, it showed New York as a city in the midst of recovery, where as in Man of Steel, everything is back to normal.
There were also 5 of them, where Superman was just one guy. And his hands were completely full just taking on Zod; there wasn't much time to coordinate anything with the local police. At least not that I ever saw.
I do agree we probably should have seen a bit more concern from Superman during the battle though, and maybe some shots of him afterwards helping out with the recovery effort.