Difference between Come off one’s perch and Fall off one’s perch

come off one’s perch —(coll.) adopt a less arrogant manner (also: get off one’s perch):

• What you’ve first got to do is to come off your perch—and listen to what we want.

fall off one’s perch —(coll., dated) die:

• By the time I fall off my perch, Britain may well be a republic.