Groups and Spaces have slightly different characteristics and features. This slide deck will help you decide which container will meet your needs the best.
You'll typically have a combination of spaces and groups on your site. Spaces will be created by admins and will represent hierarchical/departmental topics. Groups can be created by both users and admins around any topic of interest. Since groups are built around membership, they make a great container for regional user group collaboration or for collaborating privately with a select set of users.