Pages can't interact with others in the same capacity as regular Facebook profiles, but some authors prefer them because there is no limit to the number of likes or followers, whereas with a Facebook profile you're capped at 5,000 friends. And with an author page you're set up as an author and Facebook doesn't get bent out of shape that you're using a pen name, so there's less chance of the inevitable Facebook trolls who report author profiles as "fake" names. I've seen too many authors lose their Facebook profile, or be forced to use their real names because Facebook is weird like that.
I do get friend requests from people who have liked my author page, but not always. Some people only follow the page, and not all my profile friends have liked or followed my author page.
Yes, I update both my profile and my author page, but it's very easy to switch back and forth. You don't have to sign out and sign back in again. Some authors even have pages set up for each of their series, but I tried that and found it was overkill. Also, I have my author page set to tweet the updates automatically, so I'm rarely on Twitter even though my tweets go out all day. That saves me time.
I also have a Facebook account now for Ravenna Tate, but since her first book won't be out until sometime next month (or later) at Evernight, I haven't done much on her profile. I do have to sign out and sign back in again to use that one, but it takes only a few seconds to do it, so it doesn't really add much time to my promo.
Hope this helps.