You can drive traffic from facebook page more than groups. Groups are more focused to spamming rather than active involvement of users.
As per my experience Facebook group is the best way to drive traffic. Promote your business in others group and create your own group as well.
Deciding on a group or a page is probably going to boil down to what you’re trying to accomplish. If you’re part of an organizing needed an entire group for business, a group might be the best fit for you. Whereas brands doing business is better with a page to show its presence.
Page information and posts are public and generally available to everyone on Facebook. In addition to an open setting, more privacy settings are available for groups. In secret and closed groups, posts are only visible to group members.