Edit [January 8, 2009] - As of right now, according to Jeff (the commenter below), the suggestion that Pages do not, infact, inform about the News Feed (just the Live Feed), is not true.
What has your experience been?
I've been helping out SPACE Gallery - nonprofit arts and music venue based in Portland, Maine - with their social media maintenance. Just now they called me with a "Facebook emergency" that none of us had foreseen, and in doing so, helped to define for me the most-fundamental difference between maintaining a fan page versus a group. They had decided that, after maintaining a page and a group, it was time to move over to one or the other, ultimately deciding that they would retain the page - that is until they realized that the group was serving them in a way they hadn't realized a page could not.
Let me explain.
Unless you're a music or art junkie, you might very well end up at shows and events the way that most people do: you're persuaded by an over-anxious friend, a fan, to get off the couch, interrupt your Netflix-enabled marathon of The Wire, and go to a show. For example, this week there's a fabulous band called Kino Proby playing in Portland, and I'm emailing all of my friends, informing folks via various status updates, tweeting, and doing everything within my digital, P2P power to ensure that my couch/TV-on-a-Friday-night friends will come out. If I don't, because they're not going straight to Kino Proby's site in order to keep up with the band's shenanigans, they'd allow themselves to live on in ignorant bliss.
SPACE Gallery relies on this set of devotees to reach out to their friends (as do all venues and galleries), offline and on. However, since not all fans are total fanatics, the Internet enables a venue to be able to rely on their core supporters and advocates to reach out passively to a wider base. Thus, for the venue, it's nice when the folks in your group RSVP for your events, this shows up in their news feeds, and their friends passively see and learn about the events as a result. It's a mildly viral way to ensure that the word is spreading without counting on putting a ton of effort into person-to-person outreach:
"Oh. I see on my news feed that 5 of my friends are going to the Mission of Burma show later on the month and that it's hosted by SPACE Gallery. How nice. I don't really like them all that much, but that blonde girl who wears Chucks in the winter and has a sense of humor like Chelsea Handler - the one I Facebook stalk - will be there and I can go and pretend that I know a thing or two about indie rock and I'll buy her a PBR."
With pages, which are totally neat looking and allow administrators to message to as many fans as desired, does not allow for this. This isn't necessarily obvious, either. It's something that, in SPACE's case, at least, was discovered through trial and error, especially since its an issue pretty specific to bands and venues (most "public figures" don't often have a roster of events they hope to promote virally), it's hard to find any note of this nuanced difference when researching the two options.(Please see the note preceding the entry for info on this edit)
Thus, if you're a venue or a band and you're interested in getting the word out organically via Facebook, it's important to keep this in mind.
Two other points on a related note:
Facebook group and page bet practices
Social Media Explorer does a wonderful job contrasting the two options. They've constructed a table which lists the pros and cons of each (built upon a sufficient, though not comprehensive table constructed by Search Engine Journal).
Also, this is, not taking the above into consideration, a pretty good argument on the behalf of changes made by Samuel Cousins, a SPACE Gallery "fan":
Facebook's plan (which I generally agree with) is that you have a group when you have a bunch of people of equal status sharing information and events and you have a fan page when you've got one central figure (SPACE) that's sharing information with its members/fans. I think the latter is more appropriate.
Also, using the fan page, there's a nicer distinction between Space-created content and fan-created content.
There are other benefits for using the fan page as well - like the stats, and targeted messaging. This is administrivia - very useful stuff for you, but not something the fans are going to wow over.