Good question! That is something we have gone back and forth about at Coastal Community Foundation. I want to give you my opinion on groups versus pages and invite your feedback. One thing we learned the hard way is that your page category cannot be changed. Currently, we are listed as “other business” and are hoping that someday Facebook will let us change to our category to nonprofit. What we do like about pages is that it automatically pulls in the foundation’s blog posts. Pages also have some more advanced features, allowing you to add applications (“widgets”).
There are definitely some advantages to groups as well and you may want to check out Center for Women as an example of an effective group. Groups make it easier to send out “bulk invites” and are a little better for viral marketing (meaning that group members can also send bulk invites to their friends).
Either way, both pages and groups allow for discussions and let you message all members (groups) and fans (page). Before you set up your group or page, take a look around Facebook to see what others are doing. Then, decide what works best for you strategically.