The new subscribe feature of Facebook seems to have lot in common with Twitter but with one key difference - if you follow someone on Twitter, you get to see all their shares whereas if you subscribe to someone on Facebook, you only see stuff that they have specifically made 'public.'
Today, Facebook has added a new feature where they recommend you other public Facebook profiles to subscribe to and these recommendations are probably based on your existing subscriptions (see screenshot). Twitter too has a similar recommendation engine which offers suggestions based on who you are currently following.
Twitter has a valid reason to worry here. They just touched 100 million users while Facebook has a 750+ million user base and people spend more time on Facebook than any other site on the web. Twitter only recently added support for multimedia while Facebook does a far better job at rendering shared content with rich snippets and inline previews.
I created my Twitter account some five years and it has taken me all this time to reach a few thousand followers. I enabled subscriptions for my Facebook profile a few days ago and the number of subscribers has already crossed the first thousand mark. That's just because of the sheer reach of Facebook.