The biggest question, of course, is how powerful they are, compared to normal humans. Though that would have some caveats based on whether normal humans can get their hands on technology produced by some Gadgeteers, super-technology-makers -- and technology that can be maintained by normal humans.
But first the question would be, for the most powerful supers, whether a super could be stopped by normal humans, or a small team of them. And if so, whether it would be feasible, how serious the situation would have to be before it would be prudent, and how much resources it would take. The "most powerful" question arises because if you had thousands of people who are marginally stronger than is normally possible, it will not affect that half a dozen Superman-strong characters are running about. (And likewise with powers that do not lend themselves to crime or crime fighting.)
The less normals can take on supers, the more need there is for the supers to police themselves. Which means the more need to make laws to allow that. Even if you have supers with Superman's ethics as well as his powers, you probably would not want the same training as for a regular police officer; it would be a waste to have a super doing work that doesn't need the powers. Less -- compliant supers would mean more flexibility, perhaps down to and including toleration of vigilantism.
Gadgeteers would shift the level of power needed downward, but unless the gadgets last forever and are plentiful, not entirely.
The more super powers there are, of course, the less of a problem, because there's a greater mass to recruit police forces from. Assuming that a slice of the general population has the powers.