Are you charging with the original 2A charger brick with the USB 3.0? USB 3.0 will give 900mA instead of the 500mA that USB 2.0 give.
4 hours screen on time with the apps you have sounds right. If you want even twice that, even up to 13 hours of screen on time - get double capacity batteries of 6500-6800mAh at$9. They’re worth it without having to change or charge the battery during the day. You even have a choice of 9000-10000mAh if you want at$35.
My Battery Observation:-
I am having Lollipop 5.0 on my Note 3(N9000). I observed that in my day to day usage, It gives me 4 hrs. of Screen on Time. My daily usage consist of Whatsapp, Facebook, Boom Beach, Clash of Clan, Gallery, Mobile data & Wi-Fi, etc. Is anyone is getting more Screen on Time? How much screen on time do u get on Kitkat?
Battery Charging:-
Once I drained my battery to 0%. I kept the Note 3 for charging in switch off mode using supplied charger in box. With my constant attention, I observed that, It is charging 1% per 1 min up to 90% and after that it takes 5 min per 1%. So 90% battery gets charged in 90 mins i.e. 1 hr. 30 mins and after that full battery(100%) gets charged in 140 mins i.e. 2 hrs. 20 mins. Which is amazing.
How is the battery charging in Kitkat?
Is Kitkat is giving more battery backup than lollipop?
Please mention your screen on time.