There is a variety of approved ammunition (9mm and 5.56) which can be tailored to various mission and weapon parameters.
Also, there is a large differece between LE ammuntion legality (HP's) and military use in various capacities. HP's are able to be used within certain applications, with all the right sign-off's.
There can be a range used as well even within specific units, ODA's, etc., depending on weapon selection. All the basics are reviewed in developing the opplan and then weapon/ammo selections are made from there.
In the LE world, though, usually the agency issued ammunition is based on a combo of factors such as performance, costs, testing by end user or other agency. One hears a lot of "cause that what the "insert high speed tactical unit name here" use, and that's good enough for us"!