That's a vague question because we don't even know the relationship the hero and villain would have. Are we talking about a world such as depicted in the 90s Batman animated series? It's a world where the yin and yang exist, but Batman almost always manages to save the lives that a villain like the Joker would put in harm's way. The interesting thing when you re-watch the series as an adult, you begin to understand how tame it is compared to the standards of the genre of today. Bruce Timm and Paul Dini gave the illusion that these villains were murderous monsters to uninitiated, but with their fresh eye they managed to invoke a little bit of empathy for the villains.
A world in which heroes and villains coexist as you describe would be a lot closer to Nolan's vision of Batman if anything else. Death, paranoia, and anarchy would be more prevalent in society. Although there has been a lot of destruction in the Marvel cinematic universe, you don't get the sense that the world is really negatively affected by this rise of meta-humans. If superheroes and villains existed in our world, which no one would be able to control, then there would be fundamental changes to the way governments and society would function. It would probably be not for the better.
Basically you'd have the ending of Watchmen, instead of the alien squid uniting the world together, it would be the relationship between superheroes and villains. We'd all be so deathly afraid because we would be like flies to them.