Same problem here
I have the same problem.
I've always had great battery life on the note 3 and right after the update I didn't notice any changes for the first few days.
Today I noticed that 5 minutes after I disconnect it from the overnight charge (was 100%) it dropped to 98%.
10 minutes after, after a bathroom break, it was already 95%. Now this is when it's idle.
I had some update notifications for a few applications (like 10 small apps, google apps and whatnot), started updating, took like 5 minutes, and it dropped to 90%.
Before the update the battery would've handled those without losing 5%.
In addition, when playing games, the battery drained so fast in comparison to 4.3.
Opening and exiting clash of clans (without any gameplay), took 1%-2% off the battery every time.
I know what you're thinking, something is wrong with the battery. But this is a new device, bought in January and had no problems with it before the update.