I couldn't tell you what the comic book versions of them are like (which are many and varied) but superheroes as modern stuff like The Avengers films, I'd say they are more like spec ops / CIA than cops but that doesn't make it any better. They often work in narratives that justify their extrajudicial use of force by making the villain be someone who is comically evil, which is shared with other copaganda.
As a cultural phenomenon, I think superheroes largely came out of US imperialism at its height, so that should tell you something about the nature of them. For good or ill, an expression of the US grappling with the idea of being so powerful it can use force to resolve just about any situation and so into violence that it is willing to do that. From there, it's a matter of whether you couch it in a narrative that justifies the violence, or you reject that narrative and play with the idea of the superhero who causes more problems than they solve.
Either way, I've never heard of, like, a superhero whose power is being really good at diplomacy or something like that. It seems to always be powers that, even if not directly related to combat, could be very useful in a fight. I don't think superheroes make much sense in a context where crime is uncommon and society actively addresses common sources of crime, like by fixing poverty and such. From that standpoint, you could argue they are a bit like super cops, since cops (though they are always needed in some form even if they're called community defense or whatever) are needed a lot less if society is peaceful and equitable.