"Es mejor tener calma que preocuparse" is a general statement. The subject, preocuparse, is impersonal (not referring to any surviving person) and if we used nos instead, we'd be specifying someone.
Now, there's nothing wrong doing that. You can absolutely say es mejor tener calma que preocuparnos, but there you have a personal infinitive with a matching reflexive pronoun. Note that this structure may sound agrammatical to some Spanish speakers, but it is accepted. The most common –and universal— way to specify a subject is to use a subordinate clause: es mejor que tengamos calma que que nos preocupemos (the double que is not a typo — one is for the comparison, the other is the relative pronoun).
Compare that to no debemos preocuparnos. The infinitive there necessarily refers to us, it cannot be impersonal, and therefore must use nos. Consider too the proclitic form: no nos debemos preocupar, clearly, using se there doesn't work.