The huge difference is that in most other countries the transport police are autonomous from any single actor and not part of or beholden to a single corporation.
Amtrak is defacto a government agency, calling it a corporation is a bit of rhetorical overkill. And since Amtrak is responsible for all long distance train travel in this country, and its infrastructure, why not have its own police force?
Is that a good thing? Why not have a Federal Rail Transport Police? I'm honestly not sure how I feel about a bunch of for profit organizations all having their own police force, but I'm willing to be convinced it's a good idea.
Something about the phrase $COMPANY Police just makes me uncomfortable.
The Federal government generally stays away from general police duties, because most of the laws typically enforced by the police are state laws. When the Feds operate police forces, it is scoped to a specific institution or place. The VA, GSA, US Mint, etc operation police forces oriented towards federal property.
I think it makes sense for railroads to have police, as the crimes that affect them are multi-jurisdictional by nature and specific to the railroad. Colleges are similar in many ways... US Marshalls + pinkertons provided security to railroads in the 19th century. Professional police alleviate many of the abuses that inevitably happen with security people.
I get a little uncomfortable with private police not tied to an institution. When I was in vacation in South Carolina, the resort rent-a-cops were sworn officers... that sounds like a way to cover up crime to me.
Interesting, forgot about CSX, though I don't count transit police in the same category as police for freight rail-freight being genuine private companies as opposed to public transit agencies.
How does it differ from other corporations with government investors?
These companies exist to be able to operate at a loss to serve a greater benefit to the public, but giving them more power than that doesn't really seem like it would be in the public's interest.