What are the advantages of adding a like button specifcally for your website if you already have a facebook page?

What i mean is say you have a facebook page for your product, and you include a like button on your website for that facebook page. Is there much point adding a like button specifically for the website as well?

The only advantage i can think of is if users like both the page and the website, it will generate an extra message in their friends news feeds, so help publicise your product a bit more.

I guess another advantage might be if facebook shuts down your facebook page for whatever reason, at least you should still have the likes for the website.

Anyone got any other good reasons for it?