I have a SGS2 international version, after the update pushed via kies to 4.1.2 I enjoyed great battery life AFTER I wiped my device clean, did reinstall then reinstalled apps.
Before that, battery life was 2-3 hrs! Really! Before i had 10-15 hrs heavy use.
The only problem was mobile connectivity, after a bunch of searches, I came up with this that worked:
Manually configure APN settings
You can create a new Access Point Network setting. Try the following.
From the Home screen, tap Menu.
Tap Settings.
Select Wireless and networks.
Select Mobile networks.
Select Access Point Names.
Tap Menu.
Tap New APN.
Complete the following fields:
Select Name. Type any name you want which will allow you to identify your connection (Example: TELUS 2011).
Tap OK.
Select APN.
Type sp.telus.com
Tap OK.
Select Proxy.
Type 74.49.0.18
Tap OK.
Select Port.
Type 80.
Tap OK.
Tap Menu.
Tap Save.
From the Access Point Names screen, select the new APN you just created.
Restart your smartphone.
Your new Access Point is created.
This worked perfectly. All the others, turn wireless off, airplane mode, restart, whatever did NOT, this did.
GT I9100 international version, unlocked, on Telus (canada sim)
4.1.2 official
I9100 HMSI