"The schoolchildren calmed down."
Translation:Elevene kom til ro.
If you are giving those as commands to settle down/calm down I would say that "Kom til ro" is something a teacher would say to his class, one person standing in front of an audience. It's a more authoritative command.
"Ro dere ned" has a slight element of things out of hand. A parent yelling at the kids, some security guard taking control over a brawl.
But in the example you ask I think they are equal, maybe "roet seg ned" could imply they calmed down on their own and "kom til ro" is after being told to calm down.