Facebook Group vs. Fan Page?

I've been working with several different organizations on Facebook pages, and the question has come up - "should I have a group or a fan page?" They have different strengths, and in some cases both may be appropriate for an organization.

With the new look for fan pages, one big plus is the ability to post a status update that will show up in your fans' home page feeds. It's a great way to get the word out about something new, put a personality on your brand or share a blog post link with your fan base.

Groups have a super easy way for a group member to invite their friends into the group - making the viral marketing part of Facebook much easier. Fan pages lack this ability, but you can use Facebook pay per click advertising to build your fan base.

Here's a link to a post from Search Engine Journal last October that also discusses the issue and their experiment. For search geeks (like me) it's particularly interesting that the fan pages are indexed by the search engines, and groups are not.

Now, as to what I said about some organizations needing both, one reason is I think it makes sense to use a group to virally build membership and then invite your group members over to your fan page. I don't see a downside to having two ways for someone to find your organization! Any thoughts?