There are a number of factors you need to consider when choosing which is right for your project, a Page or a group.
Personal vs. Corporate:
Due to their security features, and size limitations (only groups under 5,000 members can send email blasts), Facebook Groups are set up for more personal interaction. Groups are also directly connected to the people who administer them, meaning that activities that go on there could reflect on you personally. Pages, on the other hand, don’t list the names of administrators, and are thought of as a person, almost like a corporate entity is considered a ‘person’ under the law.
Facebook considers groups to be an extension of your personal actions. When you post something as a group administrator, it appears to be coming from you and is attached to your personal profile. Alternately, Pages can create content that comes from the Page itself, so that content doesn’t have to be linked to you personally.
Email vs. Updates:
As long as a group is under 5,000 members, group admins can send messages to the group members that will appear in their inboxes. Page admins can send updates to fans through the Page, and these updates will appear in the “Updates” section of fans’ inboxes. There is no limit on how many fans you may send an update to, or how many total fans a Page can have.
Groups offer far more control over who gets to participate. Permissions settings make it possible for group admins to restrict access to a group, so that new members have to be approved. Access to a Page, however, can only be restricted by certain ages and locations. Again, this makes groups more like a private club.
Pages can host applications, so a Page can essentially be more personalized and show more content. Groups can’t do this.
Neither Groups nor Pages have great moderation features. They can both be a little granular as to how things get posted, who can post, and what kind of media can be posted, but that’s about it.