For class on Tuesday night, everyone created a Google Group. Creating the group was easy for me. Then we had to collaborate within our individual small groups and do some "chores" through one person's group. This was kind of confusing for some people, but I think we got it all worked out in the end.
As a learning tool, I definitely think that using a Google Doc is easier than using a Group. I say this because in a Group, only one person can edit a document at any one time. It can get frustrating to be "locked out" of a document because someone else in your group is editing it at that time. With a Google Doc, multiple people can edit at the same time. This is especially useful if there are many people in your group.