I will discuss police detectives. The pros of being a detective compared to a beat cop are that it is a promotion, with more pay and prestige. Detectives have more flexibility, and answer directly to the lieutenant. Detectives rely on skill and investigative strategies, as well as close work with forensic technicians. They have to be abreast of technology in all forms, including the use of the Internet for crime. They also have to be able to use "old-school" traditional methods. This makes detective work challenging and interesting.
The cons of detective work are the long hours and high stress of the job. The pay is higher than beat cops, but still low considering the time and effort required. Being a detective is trying on family members. You can be called at any time, including from a family gathering or in the middle of the night. It is hard for family to understand the emotional aspect of detective work. Detectives often face psychological problems from stress and having to cope with seeing the worst of human nature.
I will assume that you are asking in this question about private detectives. However, it is not clear whether you are asking about the pros and cons of being a detective or of having detectives. I will assume the latter.
The presence of private detectives can be a good thing. There are many people who have problems for which they need the services of a detective but who cannot get police help because their problems are not important enough to warrant police attention. As an example, a person whose teenaged child has gone missing may have more luck hiring a detective to help find the child than they would have if they relied on the police.
On the other hand, it is possible that private detectives constitute a threat to the general public at times. They may act in ways that invade the privacy of members of the public. For example, if they are trying to prove someone's spouse is cheating on them, they might try to take pictures of the private behavior of that spouse and his or her friends.
I hope this is the sort of thing you are looking for. If not, please clarify your question.