One of my clients asked me to clarify the differences between Facebook  Groups and Pages, therefore I thought it would be handy to share this  with you too! 
As many of you will have noticed, Facebook have  created a new design for new Groups being created and some new  functions to Pages.
There are benefits to  both – my  preference is Pages( due to the nature of the clients I work with and  what they need to achieve) – however if  you need to have  two way/group  communication with your  audience then groups are more  suitable.
Here is my summary:
Pages
You  can:
- Monitor the insights/analytics for the page – this is great for monitoring the activity on the page
 - Get ‘widgets’ and ‘like streams’ for your website – therefore allowing people to ‘like’ the page directly from your website/blog
 - Get a username for your page, therefore being able to direct them straight to the page, without having to rely on Facebook’s search engine (eg www.facebook.com/SocialMediaMarketingSouthWales)
 - Be logged in as your facebook page and comment/like other business pages (this is a new feature since we had the coaching session)
 - Get notifications if someone comments or likes on any content of your page (another new feature)
 - Update the wall so that it will appear in the fans news feed
 - Add applications such as Reviews, Networked Blogs, Customised Applications, Online shop – giving the page more functionality
 
Groups
You  can:
- Add people to the group from your friends list without their prior permission (as a Facebook user who has had this done to them, it is quite annoying)
 - Updates will appear as a notification rather than appear naturally in your news feed (this setting can be changed, but again, quite annoying in the first instance)
 - Chat with other members of the group using online chat (even if you aren’t friends with them)
 - Create documents to be stored on the group and edited by multiple people
 - Keep groups secret and only allow selected people to join the group
 - Set up a group email address so that any emails sent to that address will go to all members within the group
 
Hope  this answers  your questions you may have on this subject?  I might  have missed a couple of things, therefore here is some  more information  from Facebook direct https://www.facebook.com/help/?page=1193