Well it is your world...
Have you ever read the Watchmen or Astro City? If you haven't, you need to run, right now, without delay, to the book store and buy the Watchmen graphic novel and look for any and all Astro City material you can find. Both of these are considered the quintessential settings of what the world would be like with supers are more than just a set of powers. Watchmen only has one real super powered individual. The others are basically normals with lots of training. Astro City is more four color but treats supers as more of a side story than the primary focus.
Anyway, I think you should go with what you think works best for your setting. That is the problem with writing by committee; you don't always get the best story for one's setting. If you do the whole thing, setting, plots, characters, etc by committee you can get some real cool stories. Which brings me to the other series that is a must read, and I would even put it before the aforementioned ones - Wild Cards. If you haven't read the Wild Cards series that is another huge asset. Supers come into existence shortly after WWII though so their impact isn't felt until after that period.
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) how many relate to the Dark Knight .... a vigilante crime fighter who runs around and says "I'm Batman" ... so real world settings merely make this surreal world a bit more like..."Hey ... it could happen... " ... 
