Android Central, finding performance issues across multiple phones, determined the Facebook app to be the primary culprit. Uninstalling it, it found the issues were "gone entirely". I've had issues myself on my Moto G recently so naturally I gave it a go, at which point I did indeed experience majorly improved performance.
You might be thinking, "Well that's no good to me -- I need my Facebook to live." Turns out the Facebook mobile website is pretty great, and if you access it via Chrome, you still get notifications. For the chat aspect, you can simply use the Messenger app only. There are some features hardcore users will miss, but most should be plenty satisfied.