I just want to ask this question to get a yes no answer on something that I've been wondering on lately.

So regarding how there are countless numbers of sites now that use the no-follow; making it harder to get ranking for your page if your website information might be something useful and will get traffic but maybe isn't something that your business connections share content of; but I am trying to find out if the benefit to having a bunch of say "likes" to your facebook page, but all the connection to your website's content isn't passing any benefit to your main page. So are you then competing with your own website in regards to SERPs to your facebook page and that of your home page. Am I correct on this; that if you start having your facebook page doing real good as far as connections and likes (helping bump up your facebook PageRank) but if you have links on your page with certain optimized keywords, that there is no benefit to your website (other than people getting to your facebook page, and then more likely to click to your page).

Hope I explained it well what I am asking. Just wanted to get a better picture of this to know what I want to focus on as far as how I'll be linking to my desired landing pages in the future.