S3 4.3 work around. The problem seems to be due to memory usage. The 3.0.31 kernel is relatively inefficient space wise. One of the feature in the 4.3 update is a process called kswapd0 which swaps process out of memory to the sd card swap space. That's it's job, make more free memory by moving relatively inactive process to swap. The process, to use an old term, thrashes if the free memory is less than ~150MB. It moves processes constantly back and forth. This thrashing uses cpu time and power. That's why the biggest power user is the OS and not the screen (which is the normal power muncher). This is why some people are reporting no problems with 4.3, they have enough headroom memory wise. This is probably why the S4 is ok with it. So if you disable active apps that you don't need and free up 200MB say, you get a quick smooth S3. No big wakeup delay, no eat the battery and no high bit rate MP3 playback stutter when the screen is locked. The kitkat kernel is a lot more efficient with space, so would solve this problem. Once Samsung tweaks kswapd0 or uses the kitkat kernel (if that's possible), to fix 4.3, you can goto 'app manager', 'disabled apps' and enable them all again, provided there is enough headroom in the Samsung fix that is.
Check out
Samsung GS3 4.3 OTA/KIES Update Problems - Samsung - Android phones TonkleChicken he/she put me on to this and after I investigating I agreed.
It doesn't fix the download notification bug however. I worked round this by disabling the download manager notifications. Not perfect I know, no down load notifications any more. If you want to do this tap and hold down the repeating notification, an 'app info' tab will appear. Tap this tab and your in the 'app manager' at the correct process, the 'download manager'. Uncheck show notifications. You can enable this again when Samsung fix it.
Hope that helps. Don't blame me if it doesn't, I didn't release 4.3.