What is the advantage of using Facebook to keep in touch with people that I'm missing?
Being able to easily react to any status that your friends post, and being able to comment on that. The email equivalent would be a separate email thread for each status update from each friend. That would quickly get messy.
And a big one for me is being able to create an event, and invite friends to it. Any updates to said event can then be communicated to all those interested without you having to make updates to a list of email addresses.
Facebook also serves as an auto-updated contact list. If I update my email or phone number, many of my contacts won't have the new information. FB doesn't have that problem. In fact I can put my phone number and email on my FB profile and my contacts can optionally auto-sync that info right to their phones so it is always up-to-date. It's possible to be "friends" with someone but not "follow" them so you don't see their posts in your normal timeline but you still get their contact info. You can also make closed or open groups which are helpful for event planning and multicast messages, and "friend lists" which let you customize the reach of each post. I guess you could do that last one with email too.