All Meetup groups have to be face-to-face group with the intention of physically meeting, so if you want to organize your online play-by-email board games or whatever, or other groups that don't actually intend to meet very often (e.g. class alumni groups mostly for the purpose of distributing info), you can't have either of those be a Meetup group.
But Facebook doesn't care if you do that.
allows private/hidden groups (invite only; Meetup can hide the memberlist and require approval to join but the group existence is still searchable)
free (Meetup currently charges ~$70 for 6 months; source: I'm an organizer for a Meetup group and that's our semi-annual bill. I'm not sure if the scale slides based on membership numbers. I can't find the billing email for the exact number at the moment.)
While I do like Meetup and still use it, using Facebook for small group organization also makes sense.
We have about 40-50 active and semi-active members (on Meetup), hold a fundraiser, and yet the organizers still have to chip in to make up the inevitable shortfall.
Whether or not to use Facebook (or Meetup for that matter) is something everybody gets to decide for themselves and preaching about what they should do is silly.