Background - The U.S. allocation of investigative power
In the U.S. system of government, there are a variety of ways that a potential incident or public policy issue of concern can be investigated.
A Congressional committee or newly created ad hoc commission can investigate. Congress also has investigative agencies such as the Library of Congress and the General Accountability Office (GAO) and Congressional Budget Office (CBO) that conduct investigations not specifically allocated to any particular Congressional committee.
An investigation can be conducted by criminal prosectors (specially appointed for the case, or ordinary, with or without a grand jury) or by one or more of various law enforcement agencies.
Multiple regulatory and taxation agencies in each state and in the federal government can conduct investigations and sometimes they have overlapping jurisdictions. Many executive branch agencies also have an "investigator general" to investigate their own internal affairs.
Military authorities and espionage agencies can also conduct investigations of various kinds.
Investigations can be conducted in the context of a civil lawsuit by a government or not governmental plaintiff seeking a civil remedy.
Investigations can be conducted by the media, foundations, private individuals, or other private parties. This is done with the aid of leaks of information including leaks that are illegal (to the leaking party) from government officials, from their own means of gathering facts (such as interviews and on site examinations of places where things happened), with public records laws, with press releases and with other investigative tools. This notion is reflected in the French description of the media as the Fourth Estate - i.e. a one of a handful of key components of the political process.
Certain university departments (in both public and private universities) consider many of these kinds of investigations to be valid subjects of academic research and devote considerable resources to conducting such investigations.
In general, anyone with jurisdiction to investigate can do so, even if other investigations are going on simultaneously.
Subquestions within the title question
Public v. Private Sector Investigation Authority Allocation
Do countries other than the U.S. have a different relative balance between governmental and private sector investigations?
For example, is much of the investigation done by Congressional committees and regulatory agencies and public universities in the U.S. done by private NGOs and individuals in other countries?
Governmental Investigative Power
Do countries other than the U.S. allocate governmental investigative authority in a significantly different manner? And if so, how?
For example, are there countries where only one investigation by the government can be conducted at a time? Do any countries conceptualize investigations as a branch of government on a par with the executive, legislative and judicial branches that is organized as a separate bureaucratic structure within the government? Do all legislatures have the kind of investigative power found in the U.S. Congress and state legislatures in the U.S.?
Private Sector Investigative Power
Do private sector investigators have more expanded, or more narrow, investigative laws for private parties?
For example, is there any place where there is pre-filing subpoena power in civil litigation or where the media has subpoena power or where using illegally leaked information is crime or where there is no right to access public records?
Literature Citations Welcome
Citations to any political science literature grappling with the concept of allocation of investigatory power as a topic to be considered in that framework would also be welcome.
This literature might consider, for example, that:
Too dispersed authority can lead to wasted duplicative investigative effort and inconvenience to people who are witnesses or have evidence. Also, if no one has a clear mandate to investigate something, because it is not clearly in anyone's jurisdiction, there is risk that things that should be investigated will not be investigated.
But, too centralized authority can make it possible to suppress critical facts in public policy debates (e.g. the widespread criticism of states that have only a single state run media and where a single political party actively manages and coordinates all governmental activity).
The aggregate scope of investigative power from all sources combined, also runs up against privacy rights and interests.