Groups are more engaging. Engagement is what works.
So, I will focus on pushing my group. However, a follow-up question...
Since having a page and the group linked to that page is free and easy to maintain, I presume you would also recommend having the page too? Is that not correct?
If you're looking to establish a brand and promote your business to a large number of people, it is better to promote a Facebook page.
If you're a new or small businesses looking to establish a presence, a group is better, especially if you sell niche products.