Though I already know the FB app's rep for battery and resources hogging, I still wasn't able to wrangle it in to submission. No matter what I tried with settings it would keep waking itself back up. I installed Greenify to Hibernate it and it was still coming on pretty regularly. Ultimately, while I like the conveniences it provides within Android (for posting articles to your wall, for excample), it isn't worth it. I uninstalled and so far the difference in battery has been very notcable. It's only been a day, though.
My main concern has been that I, too, had better battery life with my Droid Maxx. So, I have been comparing my use and apps phone to phone. I had FB installed on the Maxx, too.
Something is definitely up with Cell Standby. Many have higher usage in their battery stats than they did previously (again for me this was with the Maxx). It's possible that they optimized other things so that CS is only higher by comparison, while using roughly the same amount of juice. Or, it may be it needs a tweak or two for optimization.