I would disable Background processing for FB and Chrome for a couple of days and see how much it changes. I bet this is a combination of low-quality signal and background processing, cell radios are very hard on the battery if the signal comes-goes (this part isn't always obvious, it seems good at one place in a structure, but is terrible in another part). You can use an app to track this over a day, but it's also hard on the battery, but can be pretty revealing.
The downside to disabling FB background is that it'll take a few moments to refresh when you open it, not sure there is a downside to limiting Chrome background.