I run a community for pug owners. It's been around for nearly 7 years and it's a "popular" site within the pug community.
It's a completely custom site (I built the whole thing from scratch...didn't use any existing community/forum software), so it's very streamlined for the needs of our community.
But what I've found as I've started making our Facebook page more active, is that Facebook users are a lot more engaged and active. And really, our demographic is incredibly active on Facebook, so they'd almost prefer to use Facebook in many cases.
So, the thought hit me today...what if I shut down pugspot.com and made the community completely distributed? The site would still exist, but only to direct people to their community of choice (Facebook, Twitter, tumblr, etc.) to interact with us.
Would this be a great idea, or 100% awful?
Keep both but either try to integrate both or use each of those for different purposes. Not 100% sure if this kind of fragmentation would do you good but facebook page could be a good place for announcing new stuff/features/articles/contests and encouraging people to follow the link to your website.
Keep the site - create ways to drive interest / interaction to your site.
You've spent 7+ years creating a community - why would you give all the revenue opportunities away to facebook? Work hard to drive activities from facebook to your site. While facebook popularity may wane, interested pug owners will remain - and you already have invested in that community.
The website is your hub while Facebook is a point of contact. Just because the pub is amazing doesn't mean that you sell your home. Sooner or later people are going to want to come from hanging out with your brand on Facebook to going home and engaging with it.
If you can try to set up ways where Facebook and the site overlap more a "like" button for blog posts, forum, news... that sort of thing can be a start. I've even seen applications that allow more content cross-over.
I have also seen a lot of mileage gained from posting links to the most popular pages of a site (most often it's best (or pillar) content. the Fan page followers will thank you for a good link and the site gets traffic from the fans.
At the end of the day if Facebook went into administration tomorrow you would still have the site. It is your hub - protect it.
My take -
keep both. shutting down ur website will be a really bad idea. Right now there might be no takers for ur website, but what if in future someone wants to buy your website?
Kepp users engaged in fb, twitter etc.. but periodically have links of pics and articles in these sites that direct users to pug spot.. re-route the traffic back to pugspot from these social network sites might be a good thing to do ;)
My take -
Give your community the option that they prefer. Could put up a simple vote and ask for their preference.
And also evaluate the cost of running the separate website vs. the value it adds to the whole mix.
It may lead to too much fragmentation, which will jeopardise the existence of the community that you have built.
If it was me, I'd create a good Facebook page, with links both ways to your old site, and see how that goes. If people migrate to FB, then concentrate on that, but don't get rid of your website, as it probably has a lot of inbound links (check on Google) that would break if it went.