Cyanogenmod (http://www.cyanogenmod.org/), (based on AOSP, not yet really stable, no dark mode)
SlimRom (http://www.slimroms.net/), (based on AOSP,stable, performant with dark mode)
SlimRom (http://www.slimroms.net/)
Tested :
KTSGS4 (http://forum.xda-developers.com/showthread.php?t=2297379) : good performance, good app to tune but autonomy is not so good.
Best Kernel : KTSGS4.
http://www.planetegalaxy.com/le-galaxy-s4-avec-snapdragon-600-gt-i9505-roote/
TODO