FB Groups vs Fanpages, which is better and why?

I would personally go with a fan page to promote your brand/business because you have more control over your audience and more options to reach new people.

A group is better for closing off information to people who already are apart of whatever you are doing. Unless of course you want to make a generic group for people to post their business opportunity in and then have what you are promoting at the top of your group in the pinned post. That's another way of using free advertising.

You just have to remember that a lot of people will ignore posting rules in groups so that is one more thing you would have worry about if you choose that route. Hope this helps!

These days you should have both!
Fan pages are good to have only cause its possible to use paid advertising.
Then you can reach most of the people that liked the page, and you can drive them wherever you want.
Small and medium Pages are pretty useless for organic reach now.
It seems that in the last couple months FB totally killed the organic reach for pages.
I mean I have pages with quality content that get 5% organic reach.
So unless you build a real big pages, post quality stuff and do it regularly you will need to use paid ads.
Seems like FB is trying to make groups active again and not only spammy groups.
The good thing is people get auto notifications when you create a post in groups.
And if its a good group many people won't disable it.
So the organic reach is way higher compared to fan pages.
If you create a good group with good targeted content, it's possible it will become an active group.
Though you should bare in mind these kinda groups can be used for very light marketing and not pushy selling.
Its more of a focus on content and dialog, and market sometimes.

I would go with a fan page

Then you can set up a group for people who purchase your product--or for things like more detailed discussions about your topic,