I am having the same issue. Opened a ticket with Samsung and they had me do a factory reset on my Samsung Galaxy Tab 3 10.1 and that has not resolved the issue.
I am currently on 4.4.2 on the tablet and the FB app is on 13.0.xxx (I don't have it in front of me).
This problem is isolated to the FB app, right after the factory reset it was just stopping the FB app, but after about an hour it went back to resetting/restarting the entire tablet, essentially crashing the tablet whenever I try to use the FB app, or at least do almost anything in the FB app.
I have used other apps like Flixster and Redbox and others on the same tablet and they run perfectly for as long as I want to be in them.
Any thoughts on what I can do to get FB to work, this is/was one of the main reasons for the tablet for my wife.