I got my S3 more slow after Automatic Update from JB on the mobile, but then after I found the solution.
Here's to solution to get the fast and stable version of JB for your phone.
- Install Kies
- Connect your phone to kies through data cable, not from WIFI
- Data cable mode should be media device, not the kies mode.
- Open Kies then Go To Tools >>> Firmware Upgrade and Initialization
- Backup your all things then click again on Firmware Upgrade and Initialization through TOOLS.
This will make s3 smooth like butter
It will download the official software thorugh Samsung's servers, It would take hours to download the software, usually 2 hours on 4mbps Connection.
and your S3 shouldn't be rooted, this method will on work on non rooted devices.