My Note 3 has terrible battery life since the update. Can I get Kit Kat back?
You cannot go back once the new update is installed. Your battery life will probably improve once lollipop has a chance to work things out with your phone. Give it a few days of battery recharge cycles to see if things improve. If no improvement is seen then a factory reset could be done though not guaranteed to fix the problem.
I'm happy to report that after a hard-reset, my battery life is back to
normal.
Glad to hear a simple reset fixed your problem.