For a campus that may have 30,000-50,000 people on it at any given time, you do need to be able to have quick responses when an incident does occur. The campus police at my local university actually do more than a typical police department might -- sending out txt messages to all students when there is an incident or threat, update details frequently, Help Call Boxes in the parking lot for at night, etc. They even handle situations when a student pulls the alarm during finals week (something that an outside police department would not be able to rapidly respond to and would get annoyed with quickly).

Some universities even have their own fire departments. Most have medical staff on duty for students as well. Some even have dentists and optometrists, etc. They really are "small cities".

The campus police can and will shoot you. They are a real-deal police department. Most of the university shootings are ended by campus police (usually shooting the gunman).

However you sort of hinted at the fact that most campus police are a lot more lenient than city/state police. This is true in my experience -- guessing, but probably because they know who they are largely working with. Students. Drunk students, students doing dumb things, etc. Not hardened criminals most of the time. I'd probably step to far, but I'd wager campus police is a much safer line of work for an officer as well (no flip of the coin if the guy you pulled over for speeding will pull a gun on you, etc).

Edits: grammar