Don’t know which to decide?
Facebook page has a hierarchy making your posts more important than others. It’s great for one speaker on the mic with everyone else participating as listener or commentator…like hero + fans.
Facebook group makes admin and users almost same level. Where every person’s post gets the same priority. Great for discussions and community building…like a leader + trusted advisers in a conference meeting.
Brands or business that operate on numbers and constantly come up with new products and services will prefer a page. Brands or business that operate on high trust and community will be more effective with a group. With that said, ALL brands should have a Facebook page…and for the ones that want/need, can have a Facebook group.