I would say 決めている can also be used in sentences like "somebody makes it a rule to do something".
Or "somebody has decided something in thier hearts". So in this case, both (決めている/決めてある) can be used in a same way, but 決めている sounds more natural.
Examples:
彼は日曜には働かないことに決めている.
He makes it a rule not to work on Sundays.
彼は医者になろうと心に決めている.
He's set on being a doctor.
Indeed, 難しいですね!