I think Samsung s3 is a great phone! But only when its rooted.
All the Jellybean roms... the most of them, are ultra smooth and stable, aaand bugfree.
And now since 02_12, CM is nearly bugfree. I only have two issuses:
When i play music, and want to skip a track on the volumebuttons, sometimes it freezes the player.
And the second is when i use gps. Without Wlan detection, all is fine, but after using one single time the wlan detection, the gps doesnt go off again, and google maps needs a lot of energy. Only a reboot shuts the gps off.
But apart from these bugs, CM is ultra fine, smooth and battery friendly.
There is now rom who sleeps so deep!!!
So keep *****ng support CM!!!