I find that having both is a great way to drive traffic to your site because some posts get a lot of engagement and shares on groups while other posts do well on the fan page. Even today I can't figure out which one brings more traffic, sometimes it's the group and sometimes it's the fan page.
With fan pages you also rely on facebook's newsfeed algorithm whereby your posts will be shown to more of your fans depending on how much engagement you get. While on groups, it depends on whether the group has a lot of spam or not. I moderate all posts to avoid any self promotion and encourage people not to switch off their notifications by letting them know that no spam will be allowed.
In my group, I only allow posts like "Thank you for adding me..." or questions related to the topic and a few blog posts or videos that I believe will add value, I don't approve every blog post or video though, I'm really picky.
So both the fan page and group have their advantages and disadvantages so I would recommend you to use both.
