i tried installing battery saving apps and it doesnt seems to help.
Well there's your problem right there. Never install any apps that claim to improve battery life. They never ever work. Ever.
I'm surprised that no one has pointed this out yet, but you people are complaining about 6 hours screen on time with 4G being sucked down as bad?
The Note 2 is rated at 8 hours screen on time on wifi. When they test this, they manually turn off 4G and 3G and fall back to GPRS, which consumes the least amount of power.
Video Playback is rated at 11 hours. This is done with the phone put in airplane mode.
Both tests are done at 50% screen brightness.
As satch has pointed out, you need to tackle the root of the problem.
The problem, from reading the thread, is your usage habits and your expectations.
1. Do you use your phone on autobrightness outdoors/brightly lit area for the majority of the time?
2. Are you leaving 4G on all the time?
Point 1 - Autobrightness will scale your screen brightness settings automatically according to background lighting. A bright room will cause your screen to max out brightness even though it's readable at 50%.
Solution: Brightness settings to manual, lowest setting as often as possible. You'll see a big improvement.
Point 2 - Singapore's 4G network is still in it's infancy and it's spotty at it's best. What does this mean for your 4G radio? If it's on, it means that it's always seeking a 4G connection even if there's none. What does this do? It drains your battery. Same way being in a low reception area drains your battery fast.
Solution: If you're not using your phone, turn 4G off. You don't need super speeds to receive push notifications, and if you're syncing massive amounts of data on mobile data, you really should be setting it to sync on wifi only. Your wallet will thank you later. Turn on 4G only when you're surfing the web etc. Troublesome? Which is worse, having to hit the 4G toggle when you want to surf or having to scramble for a charger?
A last note is that from all the screens I can see, you guys have perfectly normal battery consumption where the screen takes up the majority of battery consumption. That is normal. This isn't your nokia 3310 days where you don't have to charge for days on end. Get used to charging every night when you get home. Manage your expectations.