I can’t locate the comment or where it was made, but someone said that they can get the same functionality out of Google+ Circles that they get out of Facebook groups. This is not true in several ways.
Circles categories are uniquely user driven and the name or function of that circle is hidden to those who are in it. Facebook Groups on the other hand have a clearly defined openly visible membership, and anyone can be added to a group by someone else without their permission. FB Groups are meant to be publicly known so you can find them, like meetup groups. G+ Circles are meant to be privately known so they are useful ways to manage the content you selectively push to people, like email distribution lists.
Going back to permissions, one of the downsides of FB Groups is that you can be added without your permission to a group that someone else selects for you. This can be awkward if you get added to a group with which you don’t want to be affiliated. The downside to G+ Circles is that there are no public circles for you to join of your own volition. The conversation is about you pushing content to a group of people you know, versus getting content from a group of people with whom you have weak or temporary ties.