Open vs. Closed Networks in Education

Something hit me today. Would I share my Twitter account, or Facebook account, etc with my boss of school principals? At the present time, honestly, I couldn't feel comfortable doing that. I whittled my issue down to one thing: closed vs. open networks. Let me explain.
closed: "friends" are limited to business related contacts.
open: "friends" can be contacts that are business related, personal friends, or people you only know online.

So, my question is this: If my use of Twitter was limited to school-related contacts (possibly including parents and students), it would be safe from outside contact, but would be less useful to me as a productive tool (weeding out things like Remember the Milk, MyMileMarker, GCal, and more). On the other hand, if Twitter was open (as it is now), professional contacts would have an uncomfortable view of my social life, yet, I could take advantage of it not only as an educational/organizational tool, but a way to keep in contact with friends, online acquaintances, and Web2.0 apps from other companies.

Which is best?