Facebook pages are like blogs, Facebook groups are like forums.
Pages are controlled by its owners, the visible posts are the ones they post in the page's name. People can comment. People can write own posts but those are hardly visible in a sidebar.
Pages' posts don't reach too many users unless you pay for advertising your posts. https://www.facebook.com/help/451485634864935
Groups are like forums.
Groups recently (they introduce it slowly throughout all groups and not instantly to all) had the horrible change that admins can only invite 250 members to events they create: https://www.facebook.com/help/167159300010051
As everywhere else, there is spam, reaching from fake users posting ads for games to marketing people promoting unrelated tech events just because they see "tech" or "developer" in your group or page title. Since users' posts get more attention in groups, groups are probably more affected by spam.
PS: Two decisions to think about:
- Do you want to link to meetup events or use the FB event system? The latter might split community activity on event pages (if there is any), the first would avoid the benefits of being in the FB system with users inviting users and users seeing events their friends go to. Also see FB's 250 invite limit for groups.
- Do you want to put every event that is on meetup on FB as well? This might be a lot of work, this might be annoying to users if there are a lot of unrelated events (the latter problem might already exist on Meetup)